Researcher ORCiD: 0000-0003-1871-7803

24 September 2024

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.

23 September 2024

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

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

The extended classical mechanics framework primarily addresses macroscopic structures and dynamics within the universe, focusing on large-scale phenomena such as gravitational dynamics, mass-energy interactions, and cosmic motion. In contrast, quantum systems operate at the micro scale, dealing with the fundamental particles and forces that govern atomic and subatomic behaviour. These two frameworks operate in fundamentally different domains, with extended classical mechanics tailored to the vast and continuous scales of the universe, while quantum mechanics addresses discrete and probabilistic interactions at the microscopic level. Therefore, the principles and applications of extended classical mechanics are distinct from those of quantum mechanics, as each framework is specifically designed to address the unique characteristics of its respective scale. As such, direct application of extended classical mechanics to quantum systems is not appropriate, given the intrinsic differences in scale, behaviour, and governing laws between macroscopic and microscopic phenomena.

Reference:

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

The concept of negative effective mass is supported by both theoretical and empirical evidence. The equation F = Mᵉᶠᶠ·aᵉᶠᶠ, where Mᵉᶠᶠ = Mᴍ − Mᵃᵖᵖ, demonstrates the inverse relationship between acceleration and effective mass, aligning with observations that apparent mass can manifest negative values when external forces are at play. This consistency extends to physical phenomena, such as the mechanical advantage gained during motion or when subjected to gravitational potential differences, where the apparent mass acts contrary to conventional mass, effectively reducing the system's inertia. Moreover, the antigravitational effects attributed to dark energy, which exhibit characteristics akin to negative effective mass, further substantiate the concept by demonstrating how such mass components can influence dynamics in both classical and extended mechanical frameworks. These observations collectively reinforce the theoretical validity of negative effective mass, highlighting its role in explaining unique physical behaviour under certain conditions.

Evidence Strengthening Extended Classical Mechanics:

Clear Connection: The research effectively demonstrates how the theoretical equation F = Mᵉᶠᶠ·aᵉᶠᶠ establishes a direct link to observed phenomena, clarifying the inverse relationship between acceleration and effective mass that can lead to negative values. The relations F ∝ aᵉᶠᶠ and inversely, aᵉᶠᶠ ∝ 1/Mᵉᶠᶠ, where Mᵉᶠᶠ = Mᴍ − Mᵃᵖᵖ, highlight that when the effective mass (Mᵉᶠᶠ) is negative, acceleration is inversely affected. This inverse relationship provides a clear explanation of the emergence of negative apparent mass, aligning theoretical predictions with empirical evidence observed in scenarios influenced by external forces, thereby enhancing the understanding of mass-energy dynamics within the extended classical mechanics framework.

Examples of Physical Phenomena: Mentioned mechanical advantage and the behaviour of systems under motion and gravitational potential differences provide tangible examples that help readers visualize the concept in action. This adds practical relevance to this theoretical discussion.

Integration of Dark Energy: Tying the concept of negative effective mass to dark energy and its antigravitational effects adds depth. This connection broadens the scope of this presentation, suggesting that negative effective mass has implications beyond just classical mechanics.

Reinforcement of Theoretical Validity: Stated that these observations collectively reinforce the validity of negative effective mass, this effectively summarize the significance of this presentation.

References:

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