Distinction Between Mechanical and Nuclear Energy: Extended Classical Mechanics.

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

24-09-2024

Mechanical energy, considered in extended classical mechanics, is distinct from nuclear energy. While dark energy and kinetic energy are forms of mechanical energy, they, along with energy involved in Lorentz transformations, do not conform to the relativistic mass-energy equation - which primarily applies to nuclear energy.

Proof of Mass-Energy Equivalence in Extended Classical Mechanics: Vol-2

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

24-09-2024

1. Introduction to Key Concepts:

The study of cosmic structures, such as the Coma cluster of galaxies observed by A. D. Chernin et al., reveals that the total gravitating mass includes contributions from ordinary matter and the effective mass of dark energy. In extended classical mechanics, a parallel concept exists where the apparent mass behaves similarly to dark energy's effective mass.

2. Understanding the Energy Components:

Within this framework, the total energy of a system consists of its potential and kinetic energy components. The potential energy integrates the contributions from both the ordinary matter mass and the apparent mass, mirroring the influence of dark energy.

3. Linking Kinetic Energy and Apparent Mass:

Analysing these components reveals that kinetic energy corresponds to the negative value of the apparent mass. This relationship shows that variations in kinetic energy are directly mirrored by the effects of the apparent mass, establishing an equivalence between them.

4. Mass-Energy Equivalence Explained:

By integrating these insights, the total energy of the system simplifies to be directly proportional to the matter mass. This relationship validates the principle that energy within a system intrinsically measures its mass.

5. Conclusion:

This approach demonstrates that mass-energy equivalence is upheld within extended classical mechanics. It reinforces the concept that mass serves as a fundamental measure of energy, incorporating kinetic and potential energies as well as contributions from dark energy dynamics observed in astrophysical phenomena.

Mathematical Presentation

1. Fundamental Equations and Observations:

According to A. D. Chernin et al.'s observations of the Coma cluster, the total gravitating mass Mɢ is given by:

Mɢ = Mᴍ + Mᴅᴇ

Where:

Mᴍ: Matter Mass (Ordinary Matter)

Mᴅᴇ: Effective Mass of Dark Energy

In extended classical mechanics, the apparent mass −Mᵃᵖᵖ functions similarly to dark energy’s mass:

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

2. Total Effective Energy Expression:

The total effective energy (Eᴛₒₜ) comprises potential energy (PE) and kinetic energy (KE):

Eᴛₒₜ = PE + KE

Where potential energy includes contributions from matter mass and apparent mass:

PE = Mᴍ + (−Mᵃᵖᵖ)

Thus:

Eᴛₒₜ = [Mᴍ + (−Mᵃᵖᵖ)] + KE

3. Resolving Kinetic Energy and Apparent Mass Relationship:

Given that:

KE = −Mᵃᵖᵖ

Substituting into the total energy expression:

Eᴛₒₜ = [Mᴍ + (−Mᵃᵖᵖ)] + KE

Simplifies to: 

Eᴛₒₜ = Mᴍ

4. Mass-Energy Equivalence Proven:

This simplification shows that the total effective energy Mᴛₒₜ is directly proportional to the matter mass Mᴍ, affirming the mass-energy equivalence principle within extended classical mechanics:

Mᴛₒₜ = Eᴛₒₜ 

Thus, the energy contained within a system directly corresponds to its mass, extending the classical understanding to encompass apparent mass and dark energy dynamics as observed in cosmic structures.

Conclusion:

The mass-energy equivalence is conclusively validated within the extended classical mechanics framework. It confirms that mass is an intrinsic measure of a system’s total energy, including contributions from dark energy dynamics and the system’s kinetic and potential energy components.

Kinetic Energy as the Counterpart of Apparent Mass: A Conceptual Equivalence in Extended Classical Mechanics - Vol-2

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

24-09-2024

The conclusion that kinetic energy (KE) equals the negative of the apparent mass (−Mᵃᵖᵖ) arises from the extended classical mechanics framework, where the total effective energy of a system includes both potential and kinetic energy components. Within this framework, potential energy incorporates contributions from the ordinary matter mass and the apparent mass, which behaves similarly to dark energy's effective mass.

When the matter mass is invariant, the total effective energy simplifies to the sum of its components. By resolving these expressions, it becomes evident that kinetic energy directly corresponds to the negative value of the apparent mass. This relationship illustrates how changes in kinetic energy mirror the apparent mass, establishing an equivalence between kinetic energy and the opposing effect of this mass within the system's energy balance.

Mathematical Presentation

Observed (Evident) Equation:

From the study by A. D. Chernin et al., "Dark Energy and the Structure of the Coma Cluster of Galaxies," the relationship between gravitating mass and its components is given by:

Mɢ = Mᴍ + Mᴅᴇ  

Where:

Mɢ: Gravitating Mass

Mᴍ: Matter Mass (Ordinary Matter)

Mᴅᴇ: Effective Mass of Dark Energy (treated as a mass equivalent to energy)

Framework of Extended Classical Mechanics:

In extended classical mechanics, the apparent mass (−Mᵃᵖᵖ) functions similarly to dark energy's effective mass. The adjusted equation is:

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

Here, the total effective energy (Eᴛₒₜ) comprises potential energy (PE) and kinetic energy (KE):

Eᴛₒₜ = PE + KE

Given the inclusion of apparent mass, potential energy is defined as:

PE = Mᴍ + (−Mᵃᵖᵖ)

Resolution:

Using the total effective energy equation:

Eᴛₒₜ = [Mᴍ + (−Mᵃᵖᵖ)] + KE

Assuming that the matter mass (Mᴍ) remains invariant, balancing the components reveals:

KE = −Mᵃᵖᵖ

Conclusion:

The kinetic energy (KE) directly corresponds to the negative value of the apparent mass (−Mᵃᵖᵖ), demonstrating a unique equivalence in extended classical mechanics. This relationship shows how energy dynamics involving apparent mass and kinetic energy establish a balance that parallels the impact of dark energy observed in astrophysical structures.

Q&A on Gravitational Dynamics, Cosmic Structures, Magnetic Fields, and High-Energy Phenomena in Extended Classical Mechanics

Extended Classical Mechanics

This comprehensive Q&A session delves into the intricacies of extended classical mechanics, exploring its unique approach to gravitational dynamics, cosmic structures, magnetic fields, and high-energy phenomena. The discussion addresses critical questions on how this framework reinterprets the formation and evolution of galaxy clusters, cosmic magnetic fields, and the behaviour of quasars and blazars. It also examines the implications of effective mass, magneto-hydrodynamics, and gravitational interactions on the large-scale structure of the universe. By integrating principles of classical physics with modern insights, this analysis provides a fresh perspective on the fundamental processes shaping the cosmos.

Click on the question links to reach the answer page.

1. How does this extended classical mechanics framework address the cosmological constant's

2. Can this extended classical mechanics framework be applied to quantum systems?

3. What evidence supports the negative effective mass concept in extended classical mechanics?

4. How does extended classical mechanics accommodate the observed isotropy and homogeneity of the universe on large scales?

5. Can the negative effective mass concept be applied to explain specific astrophysical phenomena, such as galaxy rotation curves or gravitational lensing?

6. How does extended classical mechanics address the issue of singularity and black hole physics?

7. How does extended classical mechanics predict the behaviour of gravitational waves in the context of binary black hole mergers?

8. Can the framework explain the observed baryon acoustic oscillations (BAOs) in the large-scale structure of the universe?

9. How does extended classical mechanics address the cosmological horizon problem?

10. How does extended classical mechanics predict the behaviour of cosmological perturbations and their impact on structure formation?

11. Can the framework explain the observed properties of fast radio bursts (FRBs) and gamma-ray bursts (GRBs)?

12. How does extended classical mechanics address the issue of cosmic magnetic fields and their role in structure formation?

13. Can the framework explain the observed properties of blazars and active galactic nuclei (AGN)?

14. How does extended classical mechanics predict the behaviour of galaxy clusters and super clusters?

15. Can the framework explain the observed properties of quasars and their redshift distributions?

16. How does extended classical mechanics address the cosmic microwave background (CMB) radiation and its fluctuations?

Keywords: Gravitational Dynamics, Cosmic Structures, Magnetic Fields, High-Energy Phenomena, Mass-Energy Interactions

#GravitationalDynamics, #CosmicStructures, #MagneticFields, #HighEnergyPhenomena, #MassEnergyInteractions,

1. How does this extended classical mechanics framework address the cosmological constant's role in dark energy?

This extended classical mechanics framework addresses the cosmological constant's role in dark energy by highlighting the distinct historical and conceptual differences between the two. Einstein introduced the cosmological constant (Λ) in 1917 to balance gravitational forces and prevent the universe's collapse under General Relativity, based on the assumption of a static universe. However, with the discovery of the universe's expansion, Einstein abandoned Λ, recognizing it as unnecessary for a dynamic cosmos. The later emergence of dark energy arose from observations of an accelerating universe, indicating complex, dynamic interactions far beyond the simplistic repulsive force Λ was originally intended to represent. Contrary to misconceptions that equate Λ with dark energy, the cosmological constant was not devised to explain expansion and lacks the intricate physical implications of dark energy. Extended classical mechanics further elucidates that dark energy is not a mysterious substance but a consequence of motion and gravitational dynamics, reinforcing that Λ’s static universe concept is irrelevant to the modern understanding of cosmic acceleration. Therefore, resurrecting the cosmological constant to account for dark energy misunderstands its purpose and history, highlighting its abandonment as a relic of outdated cosmological thought rather than a viable explanation for contemporary observations.

Reference:

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

 

[Return to Main Page]