Framework for Energy Manifestations in the Universe’s Mass-Energy Composition:

The study explores the universe's mass-energy composition, where 95% consists of dark energy and dark matter. Dark energy, with its distinctive property of negative pressure, drives the accelerated expansion of the universe. This work proposes an extended classical mechanics framework that integrates dark energy, dark matter, and effective mass as essential influences on cosmic structure and expansion. In this framework, effective mass is defined as a combination of positive and negative mass effects, with dark energy's negative apparent mass acting as an antigravitational force that counteracts gravitational collapse and supports expansion. 

The study reinterprets gravitational influence by relating gravitating mass (Mɢ) to both matter and effective mass, moving away from general relativity's reliance on spacetime curvature. Total energy in this model is presented as a balance between potential and kinetic energies, where potential energy embodies latent effects of cosmic fields, and kinetic energy includes dynamic mass-energy interactions. This approach offers an alternative to conventional spacetime curvature models, suggesting that cosmic mass-energy interactions can be comprehended within an extended classical mechanics framework that accounts for dark energy effects.

Soumendra Nath Thakur ¹ and Deep Bhattacharjee ²

01-11-2024

Abstract:

This study explores the total mass-energy content of the universe, revealing that approximately 5% comprises baryonic matter, while the remaining 95% consists of dark energy and dark matter. Dark energy, a major constituent, is characterized by a unique property of negative pressure, driving the accelerated expansion of the universe. This work delves into the intricate relationships among mass components—baryonic matter, dark matter, and dark energy—and examines their influence on gravitational dynamics, effective mass, and energy distribution across cosmic structures.

Keywords: Mass-Energy Composition, Dark Energy, Dark Matter, Baryonic Matter, Cosmic Dynamics, Effective Mass, Apparent Mass, Gravitational Interactions, Extended Classical Mechanics, Kinetic Energy, Potential Energy, Cosmic Expansion, Gravitational Stability, Energy Manifestations, Cosmological Principle, Negative Pressure, Mass Distribution, Gravitating Mass, Newtonian Mechanics,

Soumendra Nath Thakur ¹: Tagore’s Electronic Lab, W.B, India

Deep Bhattacharjee ²: Integrated Nano sciences Research (QLab), India, Formerly engaged with R&D EGSPL

¹ Corresponding Author: 

postmasterenator@gmail.com ; postmasterenator@telitnetwork.in 

² deepbhattacharjee.ac@gmail.com ; ² itsdeep@live.com

Funding: No specific funding was received for this work.

Potential competing interests: No potential competing interests to declare. 

1. Introduction:

The universe's mass-energy distribution is dominated by non-baryonic components, with dark energy and dark matter representing the bulk of its constituents. While dark energy accelerates cosmic expansion, dark matter contributes to the formation and stability of galaxies and clusters. This study provides an in-depth analysis of these components through an extended classical mechanics approach, highlighting key mass-energy interactions and their implications on the dynamics of large-scale structures.

2. Mass-Energy Constituents and Dark Energy in Cosmic Dynamics:

2.1 Baryonic Matter and Dark Energy Contributions:

Baryonic matter, making up only about 5% of the universe’s mass-energy content, is dwarfed by the contributions of dark energy and dark matter. Dark energy, exerting negative pressure, acts as an antigravitational force driving galactic recession and cosmic expansion.

2.2 Case Study: Coma Cluster Dynamics under Dark Energy Influence:

In "Dark Energy and the Structure of the Coma Cluster of Galaxies" by A. D. Chernin et al., researchers apply Newtonian mechanics to understand dark energy's role in the dynamics of the Coma Cluster. This analysis reveals that dark energy’s antigravitational force counteracts gravitational attraction, stabilizing the cluster and preventing collapse. The study redefines the gravitational influence by relating gravitating mass (Mɢ) to matter and effective mass, diverging from spacetime curvature interpretations in general relativity.

3. Mass Components in Extended Classical Mechanics:

The relationship among gravitating mass, matter mass, and effective mass provides a new perspective on gravitational interactions and dark energy influence. This is formalized as:

Mɢ = Mᴍ + Mᵉᶠᶠ

Where:

• Mɢ: Total gravitating mass, including both matter and effective mass contributions.
• Mᴍ: Matter mass, encompassing both baryonic and dark matter contributions.
• Mᵉᶠᶠ: Effective mass representing dark energy’s influence and any additional mass phenomena that alter gravitational dynamics.

This formulation integrates gravitational effects and dark energy, providing a robust framework for analysing gravitational interactions.

4. Apparent and Effective Mass Contributions:

4.1 Apparent Mass Dynamics:

Apparent mass within extended classical mechanics modifies Newton's equation of motion as:

F = (Mᴍ − Mᵃᵖᵖ)·aᵉᶠᶠ

where Mᵉᶠᶠ is the effective mass, combining matter mass Mᴍ and apparent mass Mᵃᵖᵖ contributions − which is negative. This reinterpretation leads to an adjusted gravitational potential, incorporating effective mass terms to account for dark energy influences, when when Mᵃᵖᵖ > Mᴍ.

4.2 Effective Mass in Gravitationally Bound Systems:

For systems like galaxy clusters, gravitational dynamics are influenced by matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ). Here, total effective mass (Mᵉᶠᶠ) includes dark matter, baryonic matter, and apparent mass, expressed as:

Mɢ = Mᴏʀᴅ + Mᴅᴍ + (−Mᵃᵖᵖ)

where: 

• Mᴏʀᴅ: Ordinary baryonic matter.
• Mᴅᴍ: Dark matter mass.
• −Mᵃᵖᵖ: Negative apparent mass from effective acceleration.

5. Uniform Matter Density and Cosmological Homogeneity:

The matter-energy distribution is uniformly dense on cosmological scales, with dark energy maintaining a constant energy density. The cosmological principle posits that, on large scales, the universe is isotropic and homogeneous. This framework supports the uniform distribution of galaxies, clustered in structures spanning millions of light-years.

The matter density, including both dark and baryonic components, is expressed as:

ρᴍ =Mᴍ,ₜₒₜₐₗ/V

where ρᴍ represents the matter density per unit volume.

6. Total Energy of the Observable Universe:

The universe’s total energy is defined as:

Eₜₒₜₐₗ,ᴜₙᵢᵥ = PEᴍᴍ,ᴜₙᵢᵥ + KEᴍᴍ,ᴜₙᵢᵥ

where:

• PEᴍᴍ,ᴜₙᵢᵥ: Potential energy from gravitational and other cosmic fields within mass-energy manifestations.
• KEᴍᴍ,ᴜₙᵢᵥ: Kinetic energy resulting from effective mass motion, possibly influenced by dark energy transformations.

In this framework, KEᴍᴍ embodies transformations linked to apparent mass and effective mass contributions, suggesting that it serves as a representation of dark energy in the extended mechanics framework. This interpretation proposes that total energy consists of potential energy PEᴍᴍ and kinetic energy KEᴍᴍ, emphasizing the dynamic interplay between these forms and their contributions to cosmic structure and expansion.

This framework treats total energy as a balance between potential and kinetic energies, with potential energy representing latent cosmic field effects and kinetic energy incorporating dynamic mass-energy interactions across the universe.

This framework also emphasizes the integration of kinetic and potential energies while suggesting that rest energy, as traditionally defined in relativity, may not be essential in understanding the broader context of energy manifestations in the universe's mass-energy composition.

7. Discussion

The study titled "The Mass-Energy Composition of the Observable Universe: Part 1 - A Framework for Potential and Kinetic Energy Manifestations" offers a nuanced look at the universe’s mass-energy components, where dark matter and dark energy substantially outweigh baryonic matter. This work deepens our understanding of the cosmos by proposing an extended classical mechanics framework that treats dark energy, dark matter, and effective mass as key constituents influencing cosmic structure and expansion.

Central to the study’s analysis is the concept of effective mass, which combines matter mass and apparent mass contributions. By defining effective mass as a sum of positive and negative mass effects, the study introduces a paradigm in which dark energy’s negative apparent mass serves as an antigravitational force that counters gravitational collapse, thereby supporting cosmic expansion. This innovative interpretation challenges conventional spacetime curvature models within general relativity, suggesting instead that mass-energy interactions can be understood through classical mechanics extended to account for dark energy effects.

A particularly insightful aspect of this study is its use of the Coma Cluster as a case study. Drawing on Chernin et al.'s work, it examines how dark energy exerts an antigravitational effect that stabilizes the cluster. The analysis indicates that dark energy plays a pivotal role in maintaining large-scale structure, as its influence manifests as a negative apparent mass (−Mᵃᵖᵖ), which adds to the cluster’s overall effective mass. This reinterpretation provides an alternative to the dark matter-centric view of galactic dynamics by attributing part of the gravitational stability to dark energy's influence on mass distribution.

Additionally, the study delves into gravitational dynamics through equations where apparent mass alters the traditional force equation, 

F = (Mᴍ − Mᵃᵖᵖ)·aᵉᶠᶠ. 

Here, apparent mass is posited as a variable that offsets ordinary matter mass under certain conditions (when Mᵃᵖᵖ > Mᴍ). 

This framework allows for a refined approach to gravitational potential in systems where dark energy and dark matter are dominant. Through these equations, the study provides a structured method for calculating total gravitating mass as a sum of ordinary matter, dark matter, and effective mass components, addressing the distinct yet interconnected roles of these masses in large-scale structures.

The study also emphasizes the cosmological principle of homogeneity and isotropy on cosmic scales, which supports the assumption that dark energy density remains constant throughout the universe. This uniformity of mass-energy distribution underscores the concept that, while dark energy is responsible for cosmic acceleration, it does so without disrupting the overall homogeneity of matter density.

In summary, the study presents a coherent model that integrates potential and kinetic energy manifestations of mass components, redefining how dark energy and dark matter contribute to cosmic expansion and stability. By extending classical mechanics to account for dark energy's negative pressure, it suggests a viable alternative to the relativistic interpretation of gravitational dynamics. This model has implications for the future study of galaxy formation, cluster dynamics, and the ultimate fate of the universe, highlighting the necessity of viewing mass-energy as an intricate blend of baryonic, dark, and effective masses in an evolving cosmic landscape.

8. Conclusion:

This study presents a structured approach to understanding the universe’s mass-energy composition, emphasizing the integration of dark matter, dark energy, and effective mass in cosmic dynamics. By redefining mass interactions within an extended classical framework, this approach highlights the dynamic role of potential and kinetic energies in shaping cosmic structure and evolution. The distinctions between effective and apparent mass provide further insight into the forces governing the universe’s large-scale motion and structure.

References

[1] 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

[2] Sanders, R. H., & McGaugh, S. S. (2002). Modified Newtonian dynamics as an alternative to dark matter. Annual Review of Astronomy and Astrophysics, 40(1), 263–317. https://doi.org/10.1146/annurev.astro.40.060401.093923

[3] Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints.Org (MDPI), 202409.1190.v2, https://doi.org/10.20944/preprints202409.1190.v2

[4] Thakur, S. N. Dark Energy as a Consequence of Gravitational and Kinetic Interactions: The Dynamic Nature of the Universe. ResearchGate, publication/384198607, https://www.researchgate.net/publication/384198607/

[5] Thakur, S. N., Bhattacharjee. D. (2024). Effective Mass of the Energetic Pre- Universe: Total Mass Dynamics from Effective and Rest Mass. ResearchGate (378298896), publication/378298896. https://doi.org/10.13140/RG.2.2.18182.18241

[6] Thakur, S. N. (2024). Mass and Effective Mass: Matter, Gravitating Mass, and Dark Energy Impacts, ResearchGate (381254461). https://www.researchgate.net/publication/381254461_Mass_and_Effective_Mass_Matter_Gravitating_Mass_and_Dark_Energy_Impacts

#MassEnergyComposition, #DarkEnergy, #DarkMatter, #BaryonicMatter, #CosmicDynamics, #EffectiveMass, #ApparentMass, #GravitationalInteractions, #ExtendedClassicalMechanics, #KineticEnergy, #PotentialEnergy, #CosmicExpansion, #GravitationalStability, #EnergyManifestations, #CosmologicalPrinciple, #NegativePressure, #MassDistribution, #GravitatingMass, #NewtonianMechanics,

Defining Energy: The Classical Forms and the Unique Nature of Relativistic Rest Energy

DOI of the study:

http://dx.doi.org/10.13140/RG.2.2.24993.62560

Soumendra Nath Thakur

Tagore's Electronic Lab, W.B, India.

30-10-2024

Abstract:

Energy is broadly defined as the capacity to perform work or induce change, manifesting in forms such as kinetic, potential, thermal, chemical, electrical, and nuclear energy. While these types adhere to principles of conservation and transformation, they typically do not alter the nuclear structure of atoms. However, the concept of relativistic rest energy, encapsulated by Einstein’s equation E =m·c², extends our understanding by regarding mass itself as a form of intrinsic energy. Unlike classical energy types, rest energy resides within the atomic nucleus and is released through nuclear processes, such as fission or fusion, where mass converts directly into energy. This paper delineates the unique qualities of rest energy in comparison to general forms of energy, highlighting the significance of mass-energy equivalence in high-energy physics.

Keywords: Energy Conservation, Kinetic Energy, Potential Energy, Thermal Energy, Chemical Energy, Electrical Energy, Nuclear Energy, Rest Energy, Relativistic Rest Energy, Mass-Energy Equivalence, High-Energy Physics, Nuclear Reactions,

Introduction:

Energy is a foundational concept in physics, commonly defined as the ability to perform work or induce change within a system. It exists in multiple forms, each corresponding to different storage, transfer, and transformation mechanisms. Whether manifested in the motion of objects, particle configurations, or molecular bonds, energy is fundamental to all physical phenomena, with the conservation of energy as a central principle in closed systems.

General Energy Forms

In classical physics, energy encompasses types such as kinetic, potential, thermal, chemical, electrical, and nuclear energy. These forms typically involve transformations without altering atomic nuclei.

• Kinetic Energy: Defined as the energy of motion, calculated as KE= (1/2)·m·v², where m is mass and v is velocity. Examples include the energy of a moving vehicle or flowing river.

• Potential Energy: This is energy based on position, condition, or configuration within a field. Gravitational potential energy depends on height, while elastic potential energy is stored in deformed materials.

• Thermal Energy: The collective random motion of particles within a substance, experienced as heat. Thermal energy flows from hotter to cooler regions, redistributing energy microscopically.

 

• Chemical Energy: Stored within chemical bonds, it is released or absorbed during reactions, as seen in fuels, food, or batteries.

• Electrical Energy: Arising from the movement of electrons, it powers numerous devices and can transform into other energy forms like light or heat.

• Nuclear Energy: Stored within atomic nuclei, nuclear energy is released in reactions like fission (splitting of nuclei) or fusion (combining nuclei), powering stars and nuclear reactors.

Force, Potential Energy, and Effective Mass in Mechanics:

In classical mechanics, the force equation F= m⋅a encapsulates how an applied force accelerates a mass, converting potential energy into kinetic energy. When elevated in a gravitational field, an object gains gravitational potential energy. This energy transforms into kinetic energy upon descent, illustrating energy transfer in mechanical systems.

In extended classical mechanics, potential energy associated with mass also introduces the concept of apparent mass, an effective mass reflecting the interplay of actual mass and the "negative" apparent mass when motion is initiated. This refined model enhances our understanding of mechanical dynamics, using an extended force equation:

F = Mᵉᶠᶠ·aᵉᶠᶠ, where Mᵉᶠᶠ = Mᴍ −Mᵃᵖᵖ

where effective mass (Mᵃᵖᵖ) reflects a system's total dynamic mass, accounting for both actual and apparent mass effects.

Total Energy in Classical Mechanics:

In classical mechanics, total energy (Eₜₒₜₐₗ) consists of the sum of potential (PE) and kinetic (KE) energy:

Eₜₒₜₐₗ = PE + KE

In extended mechanics, total energy includes additional nuances:

Eₜₒₜₐₗ = PEᴍᴍ + KEᴍᴍ

where:

• PEᴍᴍ: Potential energy within the extended classical context.

• PEᴍᴍ: Kinetic energy arising from the effective mass contribution, representing transformations influenced by apparent mass.

Rest Energy: A Relativistic Perspective

Beyond classical forms, rest energy redefines energy by establishing mass-energy equivalence. Expressed by E =m·c², rest energy reveals that mass itself embodies intrinsic energy independent of motion or position. This intrinsic energy is particularly significant in nuclear reactions, where changes in atomic nuclei release massive energy amounts.

• Rest Energy: E =m·c², where m is mass and c is the speed of light. This energy, distinct from kinetic or potential energy, is an inherent property of mass itself, highlighting the profound store of energy within atomic nuclei. 

Classical vs. Relativistic Energy: Key Differences

Unlike general energy types, which transform without altering nuclear structure, rest energy pertains specifically to nuclear-level changes where mass converts to energy. This distinction is fundamental:

• General Energy Forms: Involve atomic or molecular interactions without affecting nuclear structure.

• Rest Energy: Involves nuclear-level changes, illustrating mass-energy interchange and revealing mass as a substantial energy store.

Total Energy in Relativistic Contexts

In the relativistic framework, total energy expands to include rest energy, integrating mass as intrinsic energy with kinetic contributions:

Eₜₒₜₐₗ = √{(m·c²)² + (p·c)²} 

where m·c² represents rest energy, and p⋅c reflects kinetic contributions via momentum. This comprehensive view emphasizes the unified role of mass and energy.

Summary:

Energy, the capacity to perform work or induce change, manifests as kinetic, potential, thermal, chemical, electrical, and nuclear forms. The introduction of rest energy reframes this concept, demonstrating that mass itself is intrinsic energy, even in a stationary state. While general energy types transform without impacting atomic nuclei, rest energy is associated with mass-energy equivalence at the nuclear level, underscoring the profound unity between mass and energy in shaping the universe.

Conclusion:

This study underscores the transformative role of relativistic rest energy in expanding our understanding of energy beyond traditional forms. While kinetic, potential, thermal, chemical, electrical, and nuclear energy follow classical principles of conservation and transformation, they primarily engage in processes that leave atomic nuclei intact. In contrast, relativistic rest energy, as encapsulated by E = m·c², reveals mass itself as a fundamental form of intrinsic energy, inherent to matter regardless of motion or external conditions. This unique form of energy becomes particularly relevant in high-energy physics, where nuclear reactions convert mass into substantial energy output, illustrating mass-energy equivalence at a profound level.

The exploration of rest energy affirms that mass is not merely a measure of inertia but also a powerful energy reservoir at the nuclear level, redefining our understanding of the atomic nucleus. By integrating this relativistic perspective, physics moves toward a more comprehensive view of total energy, one that unifies mass and energy within the same framework. This insight has far-reaching implications, particularly in fields where high-energy processes and nuclear interactions are fundamental. In conclusion, the study of rest energy illuminates the extraordinary interdependence of mass and energy, advancing our grasp of the universe’s fundamental structure.

#EnergyConservation, #KineticEnergy, #PotentialEnergy, #ThermalEnergy, #ChemicalEnergy, #ElectricalEnergy, #NuclearEnergy, #RestEnergy, #RelativisticRestEnergy, #MassEnergyEquivalence, #HighEnergyPhysics, #NuclearReactions,

NOTE: Interpreting KEᴍᴍ as analogous to dark energy introduces a compelling dimension to the extended mechanics framework. It suggests that apparent mass transformations could echo the enigmatic effects of dark energy, potentially driving expansion in a similar way—quite an intriguing angle for exploring cosmological energy dynamics.