Energy Dynamics of the Universe: Negative Apparent Mass, Matter Mass, and the Negative Effective Mass of Dark Energy

The First Part

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

07-09-2024

This study title suggests a comprehensive investigation of how various types of mass and energy, including mechanical energy as interpreted in classical mechanics, interact and shape the universe's evolution and expansion.

Energy Dynamics of the Universe: This section explores how dark energy, regarded as potential energy, was the sole energetic form in the primordial universe and later regenerated through motion and gravitational dynamics following the formation of matter mass. The study includes an analysis of the motion and gravitational dynamics of mechanical energy in the context of classical mechanics. It proposes an exploration of how potential energy, kinetic energy, and more exotic forms—such as dark energy (as a form of potential energy)—interact and contribute to the universe's evolution.

Negative Apparent Mass: This term describes a theoretical concept where generated mass appears negative under specific conditions, particularly from a mechanical perspective that involves motion and gravitational dynamics within classical mechanics. This concept is vital for understanding non-intuitive gravitational effects and how such mass influences the universe's structure and expansion.

Matter Mass: This includes both baryonic matter (ordinary matter composed of protons, neutrons, and electrons) and dark matter, which is non-luminous and interacts primarily through gravity. These two forms of matter represent the majority of mass in the universe and are essential in understanding the formation and evolution of cosmic structures such as galaxies, clusters, and filaments.

Negative Effective Mass of Dark Energy: Dark energy is observed to cause the accelerated expansion of the universe, highlighting its crucial role in cosmic evolution. The term "negative effective mass" implies a framework where dark energy possesses properties that effectively counteract gravitational attraction, resulting in a repulsive effect that accelerates the universe's expansion.

Background:

The intercontinental research study, Dark Energy and the Structure of the Coma Cluster of Galaxies by A. D. Chernin et al., introduces three types of mass that are pivotal to understanding the dynamics of the cluster:

Matter Mass (Mᴍ): This represents the total mass of both dark matter and baryonic matter within the Coma Cluster, contributing to its gravitational binding.

Dark Energy Effective Mass (Mᴅᴇ): A conceptual mass that represents the effect of dark energy, characterized by negative pressure, resulting in a negative mass (Mᴅᴇ < 0) that counteracts gravitational attraction.

Gravitating Mass (Mɢ): The net mass responsible for gravitational attraction, combining the effects of matter mass and dark energy, as expressed in the equation:

Mɢ = Mᴍ + Mᴅᴇ

The total mass per unit volume, including both dark and baryonic matter, represents the density of matter mass (ρᴍ) within the Coma Cluster, which is expressed by the formula:

ρᴍ = Mₜₒₜₐₗ/V

​Our earlier research concluded that dark energy and negative apparent mass can be understood as consequences of gravitational dynamics and motion. This framework extends classical mechanics to provide a consistent and coherent explanation for gravitational interactions, accounting for phenomena associated with dark energy.

Additionally, our studies on the evolution and impact of dark energy in the universe have characterized dark energy as the potential energy of the universe, associated with a negative mass (<0). Initially, this negative mass was the driving force behind cosmic inflation and the formation of positive mass. Following this period of rapid expansion, dark energy entered a phase of hibernation as the density of gravitational mass began to exceed that of dark energy.

As the universe continued to evolve, gravitationally bound galaxies formed from regions of denser gaseous mass, leading to a reduction in the average density of this mass. The subsequent scattering of galaxies altered the motion and gravitational dynamics, allowing dark energy to regain influence in the spaces between galaxies and galactic clusters.

Currently, dark energy has reasserted its dominance in intergalactic space. The ongoing interplay between cosmic motion and gravitational dynamics enhances the effects of dark energy, resulting in the accelerated recession of gravitationally bound galaxies.

In the following sections, we will build upon our earlier conclusions that the negative effective mass of dark energy, considered as potential energy, was the sole energetic form in the primordial universe but later regenerated after a period of hibernation following the formation of matter mass. We will then link and interpret the potential energies associated with negative apparent mass and the regenerated negative effective mass of dark energy, post-hibernation, as consequences of gravitational dynamics and motion. These ideas will be discussed within the broader context of the energy dynamics of the universe, specifically focusing on Negative Apparent Mass, Matter Mass, and the Negative Effective Mass of Dark Energy.

Presentations: Analytical Description of Equations

The following equations describe the state of the universe in its primordial phase, specifically before the Big Bang event. Here is an analytical description of each equation:

Primordial Universe Before the Big Bang Event. 

Potential Energy of Negative Effective Mass: Mᴅᴇ <0: Eᴅᴇ,ᴜₙᵢᵥ = ∞ 

• The potential energy associated with the negative effective mass of dark energy, denoted as 

Eᴅᴇ,ᴜₙᵢᵥ, is infinite:

Eᴅᴇ,ᴜₙᵢᵥ = ∞ 

• This signifies that before the Big Bang, dark energy (characterized by a negative effective mass Mᴅᴇ, where Mᴅᴇ <0) dominated the universe with infinite potential energy.

Proportionality of Potential Energy:

• The total potential energy of the universe, (PEᴜₙᵢᵥ) ∝ Eᴅᴇ,ᴜₙᵢᵥ, is directly proportional to Eᴅᴇ,ᴜₙᵢᵥ:

PEᴜₙᵢᵥ ∝ Eᴅᴇ,ᴜₙᵢᵥ, 

• Given that Eᴅᴇ,ᴜₙᵢᵥ =∞, the total potential energy PEᴜₙᵢᵥ is also infinite. This indicates a state where the universe's energy content is entirely determined by the potential energy of dark energy.

Kinetic Energy of the Universe:

• At this stage, the kinetic energy of the universe, KEᴜₙᵢᵥ, is zero:

KEᴜₙᵢᵥ =0

• This implies that there was no movement or expansion happening in the primordial universe, reflecting a static state dominated solely by potential energy.

Total Energy of the Universe:

• The total energy of the universe, Eₜₒₜₐₗ,ᴜₙᵢᵥ, is composed of both potential and kinetic energy:

Eₜₒₜₐₗ,ᴜₙᵢᵥ = PEᴜₙᵢᵥ + KEᴜₙᵢᵥ = ∞ + 0 = ∞

• This reinforces the idea that the universe, in its initial state, was completely governed by the infinite potential energy of dark energy, with no kinetic contribution.

Total Mass Equivalent of the Universe:

• The total mass of the universe, Mₜₒₜₐₗ,ᴜₙᵢᵥ, is described as the sum of effective mass and matter mass:

Mₜₒₜₐₗ,ᴜₙᵢᵥ = Mᵉᶠᶠ,ᴜₙᵢᵥ + Mᴍ,ᴜₙᵢᵥ

where Mᵉᶠᶠ,ᴜₙᵢᵥ = ∞, Mᴍ,ᴜₙᵢᵥ = 0 

​

• This suggests that the universe's mass was entirely in the form of effective mass associated with dark energy, with no conventional matter yet formed.

Force Relationship in the Universe:

• The force within the universe is defined by the product of effective mass and its corresponding acceleration:

Fᴜₙᵢᵥ = Mᵉᶠᶠ,ᴜₙᵢᵥ·aᵉᶠᶠ,ᴜₙᵢᵥ 

Given that the effective mass is infinite and the matter mass is zero, the force related to dark energy's effective mass is also infinitely large.

• This infinite force would have been a driving factor in the subsequent dynamics of the universe's expansion.

Gravitational Force Relationship:

• While the gravitational force relationship is not fully defined in the presentation, it would logically be influenced by the infinitely large effective mass, indicating a dominant repulsive or expansive force in the primordial state.

Interpretation

In the primordial universe, before the Big Bang event, the cosmos existed in a state of infinite potential energy, completely dominated by dark energy's negative effective mass. This negative effective mass carried an infinite amount of potential energy, which was the only form of energy present, as there was no kinetic energy due to the absence of movement or expansion. The total energy of the universe was thus entirely governed by this boundless potential.

During this period, the universe had no conventional matter; its total mass consisted solely of the infinite effective mass associated with dark energy. This situation created an infinitely large force within the universe, stemming from the interaction of dark energy's effective mass with gravitational dynamics. The overwhelming presence of this force and energy likely set the stage for the subsequent expansion and evolution of the universe, ultimately leading to the Big Bang and the formation of matter as we know it.

Post-Big Bang Event

Potential Energy After the Big Bang:

• The potential energy of the universe, PEᴜₙᵢᵥ →0, approaches zero after the Big Bang event:

 PEᴜₙᵢᵥ →0

• This indicates that, following the Big Bang, the potential energy previously associated with dark energy's negative effective mass has diminished to negligible levels.

Kinetic Energy After the Big Bang:

• The kinetic energy of the universe, KEᴜₙᵢᵥ, becomes infinite:

KEᴜₙᵢᵥ = ∞

• This suggests that immediately after the Big Bang, the universe underwent rapid expansion, resulting in infinite kinetic energy due to the dynamic motion of matter and radiation.

Total Energy of the Universe:

• The total energy of the universe, Eₜₒₜₐₗᴜₙᵢᵥ, is the sum of potential and kinetic energy:

Eₜₒₜₐₗ,ᴜₙᵢᵥ = PEᴜₙᵢᵥ + KEᴜₙᵢᵥ = 0 +  ∞ =  ∞

• This reflects that, in the aftermath of the Big Bang, the universe’s total energy is dominated by the infinite kinetic energy, as the potential energy has become negligible.

Total Mass Equivalent of the Universe:

• The total mass of the universe, Mₜₒₜₐₗ,ᴜₙᵢᵥ, is now described solely by the matter mass:

Mₜₒₜₐₗ,ᴜₙᵢᵥ = Mᴍ

where Mᴍ represents the conventional mass of baryonic and dark matter formed after the Big Bang.

• This indicates that, after the Big Bang, the universe's total mass is comprised of matter mass, with the previous effective mass associated with dark energy no longer contributing to the mass.

Force Relationship in the Universe:

• The force within the universe can be related to the total mass and its acceleration:

Fᴜₙᵢᵥ = (Mᴍ,ᴜₙᵢᵥ + Mᵉᶠᶠ,ᴜₙᵢᵥ)·aᵉᶠᶠ,ᴜₙᵢᵥ 

Given that the matter mass Mᴍ,ᴜₙᵢᵥ is non-zero (>0) and the kinetic energy is infinite KEᴜₙᵢᵥ = ∞, the forces involved in the universe’s expansion and structure are influenced by this mass and the accelerating expansion.

Gravitational Force Relationship:

Although not fully detailed, the gravitational forces in the universe after the Big Bang would be influenced by the distribution of matter mass and the resulting gravitational dynamics, moving away from the previously dominant repulsive forces of dark energy.

Interpretation

Following the Big Bang, the universe transitioned from a primordial state of infinite potential energy to one characterized by infinite kinetic energy. This shift marks the onset of rapid expansion, where the potential energy associated with dark energy's negative effective mass became negligible, and kinetic energy surged to dominate the universe’s energy composition.

During this phase, the total energy of the universe is described by the infinite kinetic energy resulting from the initial expansion. The mass of the universe is now composed entirely of conventional matter, reflecting the formation and distribution of baryonic and dark matter in the aftermath of the Big Bang. The forces driving the universe’s evolution are now governed by this matter mass and the dynamic motion, leading to the ongoing expansion and structuring of the cosmos.

To be continued ...

#EnergyDynamicsOfUniverse, #NegativeApparentMass, #MatterMass, #NegativeEffectiveMass #DarkEnergy,

Relativistic Gravitational lensing is based on wrong idea:

06-09-2024

Gravitational lensing is not what Einstein preached and people obeyed. Space can't bend, it can't bend at all, and time can't stretch, but many preconceived people still believe what their God says about time and space. They can't just use their common sense or scientific fundamentals, they are inclined not to verify that Einstein's distorted spacetime is not scientifically valid, but is a pure misconception.

Recent research has begun to question the necessity of spacetime distortion as a fundamental concept of gravitational lensing. Instead, there is increasing recognition of the direct effect of the gravitational field on the motion of objects. where the photon's path bends due to momentum changes rather than intrinsic spacetime curvature.

Relationship between photon properties and wave speed:

E = hf; ρ = h/λ;

Change in photon energy in strong gravitational field:

Eg = E + ΔE = E − ΔE; E = Eg.

Changes in momentum and wavelength due to gravitational effects:

Eg = E + Δρ = E − Δρ = E; h/Δλ = h/−Δλ;

Correspondence of photon energy in gravitational field:

Eg = E; Δρ =−Δρ; ℓₚ/tₚ

"Relative time arises from relative frequency. It is the phase shift of relative frequencies due to the infinitesimal decay of wave energy and the corresponding increase in wavelength of oscillation; which occurs in any clock between relative positions or due to differences in gravitational potential. cause error in reading the time of a clock, which is incorrectly represented as time dilation."

#GravitationalLensing

Evolution and Impact of Dark Energy in the Universe

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

05-09-2024

Dark energy, characterized as the potential energy of the entire universe with negative mass (<0), initially drove cosmic inflation and contributed to the formation of positive mass. Following this period of rapid expansion, dark energy entered a phase of hibernation as the density of gravitational mass surpassed that of dark energy.

As the universe evolved, gravitationally bound galaxies formed from denser regions of gaseous mass, leading to a reduction in the average density of this mass. The subsequent scattering of galaxies altered the motion and gravitational dynamics of the universe, allowing dark energy to regain influence within the spaces between galaxies and galactic clusters.

Currently, dark energy has reasserted its dominance in intergalactic space. The interplay between cosmic motion and gravitational dynamics continues to enhance the effects of dark energy, leading to an accelerated recession of gravitationally bound galaxies.

In a future scenario where the distribution of gravitational mass becomes sufficiently spread across an extensively expanded universe, the generation of dark energy may cease, potentially halting further galactic recession. This reduction in dark energy could allow for the gravitational collapse of dispersed matter, potentially culminating in the formation of a new singularity.

Mathematical Presentation 

Dark Energy Characterization

• Dark Energy:  Eᴅᴇ (Potential energy with negative mass: (Mᴅᴇ<0)

Cosmic Inflation and Formation of Positive Mass

• Total Mass: Mₜₒₜₐₗ =Mᴍ + Mᴅᴇ

• Positive Mass Formation: Mₚₒₛᵢₜᵢᵥₑ > 0 (Contribution to the universe's mass)

Hibernation Phase

• Dominance Condition: ρmatter > ρᴅᴇ

• Where ρₘₐₜₜₑᵣ is the density of gravitational mass 

• ρᴅᴇ is the density of dark energy

Galaxy Formation and Dynamics

• Density Reduction:ρ𝑔𝑎𝑠𝑒𝑜𝑢𝑠_𝑚𝑎𝑠𝑠 → Decreases 

• Galactic Dynamics: Scattered galaxies alter Fᴜₙᵢᵥ = (Mᴍ + Mᵉᶠᶠᴘᵣₑₛₑₙₜ)⋅aᵉᶠᶠ

Current State

• Dominance in Intergalactic Space: Dark Energy Influence ∝ Space Between Galaxies

• Recession Acceleration: Increased aᵉᶠᶠ → Accelerated Recession of Galaxies

Future Scenario

• Spread of Gravitational Mass: ρ𝑚𝑎𝑡𝑡𝑒𝑟_𝑒𝑥𝑝𝑎𝑛𝑑𝑒𝑑 → Uniform Distribution 

• Halted Dark Energy Generation: Eᴅᴇ ceases

• Galactic Recession Halt: No Further Recession

Potential Collapse

• Gravitational Collapse: 

Diminished Dark Energy → Increased Gravity 

• Formation of New Singularity: 

Collapse of Scattered Matter → Singularity Formation

Brief Descriptions

• Dark Energy: Represents the universe's potential energy with negative mass, contributing to inflation and positive mass formation.

• Hibernation Phase: Occurs when the density of gravitational mass exceeds that of dark energy, leading to a period of reduced dark energy influence.

• Galaxy Formation: As galaxies form and scatter, the average density of matter decreases, changing cosmic dynamics and allowing dark energy to regain influence in intergalactic space.

• Current State: Dark energy now dominates intergalactic space, accelerating the recession of galaxies.

• Future Scenario: Once matter is uniformly distributed in an expanded universe, dark energy generation may cease, halting further galactic recession.

• Potential Collapse: Reduced dark energy could result in increased gravitational forces, potentially leading to the collapse of matter into a new singularity.

The concept of negative apparent mass is influenced by the observational concept of negative effective mass of dark energy.

Cite this research

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

05-09-2024

1. Gravitating Mass and Dark Energy: Research Insights

Based on the research paper, "Dark Energy and the Structure of the Coma Cluster of Galaxies" by A. D. Chernin et al., the relationship between gravitating mass, matter mass, and dark energy effective mass is expressed as:

Mɢ = Mᴍ + Mᴅᴇ,

where:

Mɢ: Gravitating Mass

Mᴍ: Matter Mass

Mᴅᴇ: Dark Energy Effective Mass (with Mᴅᴇ<0)

The concept of dark energy effective mass (Mᴅᴇ<0), while not part of classical mechanics, is derived from observational evidence and represents an extension of classical mechanics by incorporating its principles to explain phenomena associated with dark energy, which is widely interpreted as potential energy.

Similarly, the notion of negative effective mass, supported by observational evidence, introduces the mechanical concept of apparent mass in contexts such as gravitational potential or motion, which is also negative and considered potential energy. This concept extends classical mechanics, based on its foundational principles, by recognizing the similarities between dark energy and the generated apparent mass as manifestations of negative potential energy.

2. Integration of Negative Effective Mass with Classical Mechanics

Concept of Negative Effective Mass:

The introduction of the idea of negative effective mass, as in the research paper, "Dark Energy and the Structure of the Coma Cluster of Galaxies" by A. D. Chernin et al., and its connection to the concept of apparent mass in contexts like gravitational potential or motion is explored in various theoretical models, particularly those involving advanced gravitational theory and cosmology. In these models, negative effective mass is used to explain phenomena such as repulsive gravitational effects or specific acceleration conditions.

The explanation that negative effective mass leads to the concept of apparent mass aligns with these frameworks by extending classical mechanics principles to account for these effects.

Consistency with Mechanical Principles:

The study correctly applies classical mechanics principles by explaining that apparent mass in gravitational potential or motion can be considered negative and interpreted as potential energy. This aligns with the classical mechanics notion that potential energy in a gravitational field is often negative due to the convention of setting zero potential energy at infinity.

Similarly, it ties the concept of negative effective mass to mechanical principles, providing a consistent explanation within the extended framework of classical mechanics.

Recognition of Observational Evidence:

The study emphasizes that concepts such as negative effective mass and apparent mass are grounded in observational evidence. This is scientifically consistent as contemporary physics relies on empirical data to validate or modify theoretical frameworks.

Observational evidence, such as the effects attributed to dark energy (e.g., the accelerated expansion of the universe), supports the extension of classical mechanics principles to include phenomena not fully explained by classical models alone.

Avoidance of Ambiguity:

The statement avoids ambiguity by clearly indicating that dark energy effective mass is not part of classical mechanics but represents an extension based on classical principles. This distinction is crucial as it clarifies that while these concepts build on classical ideas, they are not confined to traditional classical mechanics.

The phrasing acknowledges that interpretations like dark energy and the concept of apparent mass in a negative context are forms of potential energy, representing extensions beyond the scope of conventional classical mechanics.

Conclusion:

The study is scientifically consistent because it integrates current interpretations of dark energy and negative mass with classical mechanics principles, aligns with observational evidence, and maintains clarity on the distinction between traditional mechanics and its extensions. This reflects an accurate understanding of how contemporary physics builds upon classical foundations to incorporate new phenomena.

3. Negative Effective Mass and Apparent Mass in Extended Classical Mechanics

Apparent Mass in Motion:

Apparent mass in motion in extended classical mechanics: The force F applied to an object results in acceleration a according to the equation F = Mᴍ·a. Here, acceleration a is inversely proportional to mass Mᴍ (i.e., a ∝ 1/Mᴍ). When a force acts on the object, an increase in acceleration leads to an apparent reduction in mass, characterized as negative apparent mass (Mᵃᵖᵖ<0). Consequently, the effective mass Mᵉᶠᶠ is given by:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ). 

where m is the matter mass and −Mᵃᵖᵖ represents the negative apparent mass. This effective mass Mᵉᶠᶠ influences the effective acceleration aᵉᶠᶠ.

​Consistency in Negative Apparent Mass:

The concept of negative apparent mass (Mᵃᵖᵖ<0) aligns with the dark energy effective mass as discussed in A. D. Chernin et al.'s research paper, "Dark Energy and the Structure of the Coma Cluster of Galaxies." Their study presents the relationship:

Mɢ = Mᴍ + Mᴅᴇ

where Mɢ denotes the gravitating mass, Mᴍ the matter mass, and Mᴅᴇ the dark energy effective mass.

In our study, this relationship is reinterpreted as:

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

where Mɢ represents the gravitational mass, Mᴍ the inertial mass, and −Mᵃᵖᵖ the negative apparent mass. This reinterpretation maintains consistency with the concept of negative effective mass and its implications in extended classical mechanics.

Implications in Classical Mechanics Equations:

4. Application of Apparent Mass in Motion:

In the framework of extended classical mechanics, the concept of apparent mass introduces an extended equation of motion:

F = (Mᴍ −Mᵃᵖᵖ)·aᵉᶠᶠ

F = (Mᵉᶠᶠ)·aᵉᶠᶠ 

where Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ). Here, Mᵉᶠᶠ represents the combination of matter mass Mᴍ and the negative apparent mass −Mᵃᵖᵖ.

When a force F is applied, it directly affects the effective acceleration aᵉᶠᶠ. Conversely, the effective acceleration aᵉᶠᶠ inversely affects the effective mass Mᵉᶠᶠ.

Since acceleration a is inversely proportional to the matter mass Mᴍ (i.e., a ∝ 1/Mᴍ), increased acceleration leads to an apparent reduction in the matter mass, resulting in an apparent mass Mᵃᵖᵖ <0. Consequently, the effective mass is given by:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

Thus, Mᵉᶠᶠ is influenced by the effective acceleration aᵉᶠᶠ. In other words, both the matter mass Mᴍ and the negative apparent mass −Mᵃᵖᵖ are influenced by the effective acceleration aᵉᶠᶠ.

5. Application of Apparent Mass in Gravitational Potential:

In the context of extended classical mechanics, the concept of apparent mass modifies the traditional equation for gravitational potential:

In classical mechanics, the equation is:

F𝑔 = G·(m₁·m₂)/r²

When mass m₁ is elevated to a distance r, the concept of apparent mass Mᵃᵖᵖ (which is negative) alters the effective mass Mᵉᶠᶠ. This apparent mass Mᵃᵖᵖ reduces the effective mass, resulting in an effective mass Mᵉᶠᶠ that combines the matter mass m₁ and the negative apparent mass −Mᵃᵖᵖ<0. In this framework, Mᵉᶠᶠ aligns with the dark energy effective mass Mᴅᴇ as described by A. D. Chernin et al., with the equation:

Mɢ = Mᴍ + Mᴅᴇ

which can be reinterpreted as:

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

Mɢ = Mᵉᶠᶠ 

 Here, Mɢ represents the gravitating mass, Mᴍ is the matter mass, and −Mᵃᵖᵖ denotes the negative apparent mass.

Substituting for Mᵃᵖᵖ, the gravitational force equation becomes:

F𝑔 = G·(Mɢ·M₂)/r², where Mɢ = Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

This equation is consistent with Mɢ = Mᴍ + Mᴅᴇ. Notably, when the magnitude of −Mᵃᵖᵖ exceeds Mᴍ, Mɢ becomes negative.

This approach represents the negative apparent mass (−Mᵃᵖᵖ) and the negative effective mass of dark energy (Mᴅᴇ) as arising from motion and gravitational dynamics, rather than as substances as commonly thought. This reinterpretation of apparent mass aligns with the principles of extended classical mechanics and provides a coherent framework for understanding gravitational interactions.

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 

ResearchGate URL:https://www.researchgate.net/publication/258737016_Dark_energy_and_the_structure_of_the_Coma_cluster_of_galaxies

Dark energy is a result of motion and gravitational dynamics, rather than being a substance.

Cite this research

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

05-09-2024

ResearchGate Discussion Link

Gravitating Mass and Dark Energy:

Traditional research, such as A. D. Chernin et al.'s work,' Dark energy and the structure of the Coma cluster of galaxies' describes dark energy with the equation Mɢ = Mᴍ + Mᴅᴇ, where Mᴅᴇ is the dark energy effective mass.

We reinterpret this by aligning the concept of dark energy with negative apparent mass −Mᵃᵖᵖ, leading to Mɢ = Mᴍ + (−Mᵃᵖᵖ).

Scientific Consistency:

Negative Apparent Mass and Effective Mass: These concepts are extensions of classical mechanics, derived from motion and gravitational dynamics rather than representing a physical substance.

Integration with Classical Mechanics: The negative effective mass (dark energy) and apparent mass are considered as intangible non-substances resulting from dynamic processes, aligning with the principles of classical mechanics.

Implications for Classical Mechanics Equations:

Motion: In extended classical mechanics, the force equation becomes F =(Mᴍ −Mᵃᵖᵖ)·aᵉᶠᶠ, where Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ).

Gravitational Potential: The gravitational force equation is modified to F𝑔 = G·(Mɢ·M₂)/r² accounting for both matter mass and negative apparent mass.

Conclusion: Dark energy and negative apparent mass are interpreted as consequences of gravitational dynamics and motion. This framework provides a consistent and coherent explanation for gravitational interactions, extending classical mechanics to account for phenomena associated with dark energy.

Reference: 

Thakur, S. N. (n.d.). The concept of negative apparent mass is influenced by the observational concept of negative effective mass of dark energy. https://soumendranaththakur.blogspot.com/2024/09/the-concept-of-negative-apparent-mass.html

Cite this:: 

Thakur, S. N. (n.d.-a). Dark energy is a result of motion and gravitational dynamics, rather than being a substance. https://soumendranaththakur.blogspot.com/2024/09/dark-energy-is-result-of-motion-and.html