Redefining Mass Profiles in Extended Classical Mechanics:

Date: 15 September 2024

The research titled "Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics" builds on the concept of dark energy's antigravity, aligning with the work of A.D. Chernin et al. on dark energy and the structure of the Coma Cluster of galaxies. It redefines mass profiles by introducing the concept of Apparent Mass (Mᵃᵖᵖ), a negative mass component that influences Effective Mass (Mᵉᶠᶠ). By incorporating the antigravity effects of dark energy and revising mass profiles, this study enhances the applicability of classical mechanics to cosmic structures, offering new insights into the universe's gravitational dynamics. The integration of these concepts helps to refine our understanding of cosmic phenomena and supports the development of a more comprehensive model in extended classical mechanics.

Dark Energy and the Structure of the Coma Cluster of Galaxies: Redefining Mass and Gravitational Dynamics in Extended Classical Mechanics:

The study explores the implications of dark energy on classical mechanics, focusing on its influence on gravitational dynamics and mass measurements within the framework of extended classical mechanics. Building on the ΛCDM cosmology, which models dark energy as a uniform, vacuum-like fluid, this research re-examines the structure of galaxy clusters, particularly the Coma cluster, using a theoretical framework that incorporates both dark energy and matter mass.

Recent advancements highlight the need to integrate dark energy's effects into gravitational dynamics, revealing that dark energy contributes significantly to the effective mass and influences the structure of galaxy clusters at large scales. The analysis, based on observational data and theoretical models, identifies three critical masses: matter mass Mᴍ and total gravitating mass Mɢ = Mᴍ + Mᴅᴇ , dark-energy effective mass  Mᴅᴇ (negative). This framework leads to a new matter density profile that aligns with observed data for the Coma cluster and addresses the limitations of traditional models.

The study proposes that the effective gravitating density of dark energy is negative, producing antigravity that can surpass gravitational effects on scales up to 20 Mpc. This finding challenges existing models and suggests that galaxy clusters' total size and mass must account for dark energy's influence. The analysis also revises the matter mass profiles of clusters, using a modified Hernquist profile that better matches observational data and provides more accurate estimates of cluster mass and size.

By incorporating dark energy's antigravity effects and redefining mass profiles, this work enhances classical mechanics' applicability to cosmic structures and provides new insights into the universe's gravitational dynamics. The integration of these concepts helps refine our understanding of cosmic phenomena and supports the development of a more comprehensive model of extended classical mechanics.

Keywords: dark energy, classical mechanics, galaxy clusters, Coma cluster, effective mass, gravitational dynamics, ΛCDM cosmology, antigravity, mass profiles,

#darkenergy, #classicalmechanics, #galaxyclusters, #Comacluster, #effectivemass, #gravitationaldynamics, #ΛCDMcosmology, #antigravity, #massprofiles,

Summary of Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics

The research paper "Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics," by Soumendra Nath Thakur, provides a comprehensive re-evaluation of classical mechanics by incorporating modern concepts from astrophysics and cosmology. The paper aims to extend the traditional framework of classical mechanics to address new phenomena related to gravitational dynamics, dark matter, and dark energy.

Part 1: Introduction and Overview

The first part of the paper introduces the motivation behind extending classical mechanics to include concepts like dark matter and dark energy. It outlines the need to reconcile classical mechanics with observational evidence from astrophysics, particularly in relation to the behaviour of gravitational systems on large scales.

Key Points:

• The traditional framework of classical mechanics is well-established but limited in its ability to address phenomena related to dark matter and dark energy.

• The paper proposes an extension of classical mechanics to incorporate these concepts, aiming to provide a unified framework for understanding gravitational dynamics.

Part 2: Equivalence Principle and Mass

This section discusses the equivalence principle in classical mechanics, which states that inertial mass (related to acceleration) and gravitational mass (related to gravitational interaction) are equivalent. The paper extends this principle to systems involving both normal matter and dark matter.

Key Points:

• The equivalence principle is reaffirmed, with the paper proposing that the effective gravitational mass (Mɢ) of a system reflects the combined inertial mass of normal matter and dark matter.

• The concept of matter mass (Mᴍ) is defined as the sum of baryonic matter and dark matter.

• The paper explores how gravitational dynamics can be influenced by both matter mass and the negative apparent mass associated with dark energy.

Part 3: Mathematical Presentation

This section provides a detailed mathematical treatment of the concepts introduced. It discusses the relationship between apparent mass and effective mass, including the role of negative apparent mass in gravitational dynamics.

Key Points:

• The paper redefines gravitational mass (Mɢ) to include the negative apparent mass (−Mᵃᵖᵖ), providing a revised framework for understanding gravitational interactions.

• Newton's second law and Newton's law of universal gravitation are reformulated to incorporate the effects of apparent mass.

• The discussion includes the implications of apparent mass for kinetic energy, object deformation, and relativistic effects.

Part 4: Future Directions and References

The final part outlines future research directions and provides a list of references for further reading.

Key Points:

• Future research will explore the relationship between apparent mass and kinetic energy, its impact on object deformation, and connections with relativistic Lorentz transformations.

• References include key works on dark energy, classical mechanics, and cosmology, providing a foundation for further study.

Overall Summary

The research paper represents an ambitious effort to extend classical mechanics by incorporating modern concepts from astrophysics. The main contributions of the paper include:

1. Extension of the Equivalence Principle:

• The paper extends the classical equivalence principle to systems involving both normal matter and dark matter, proposing that the effective gravitational mass of such systems is equivalent to the combined inertial mass.

2. Integration of Dark Matter and Dark Energy:

• The paper introduces the concept of negative apparent mass and integrates it with gravitational dynamics. This extension provides a framework for understanding phenomena related to dark energy and cosmic acceleration.

3. Reformulation of Gravitational Dynamics:

• Traditional equations of motion and gravitational forces are modified to include the effects of apparent mass, offering a revised approach to gravitational interactions.

4. Future Research Directions:

• The paper outlines potential areas for future research, including the impact of apparent mass on kinetic energy and its relation to relativistic effects.

Overall, the paper successfully bridges classical mechanics with modern astrophysical concepts, providing a comprehensive framework for understanding gravitational dynamics and cosmic phenomena. The proposed extensions offer valuable insights and suggest avenues for further exploration and refinement in the field of classical mechanics and cosmology.

#ExtendedClassicalMechanics

Dark Energy Effective Mass (Mᴅᴇ):

In the research paper "Dark energy and the structure of the Coma cluster of galaxies" by Chernin et al. (2013), the concept of Dark Energy Effective Mass ($M_{de}$) is introduced as part of the analysis of the Coma cluster's structure. The paper explores how dark energy, characterized by its antigravitational effects, influences the structure of galaxy clusters.

Description of Dark Energy Effective Mass:

1. Definition and Role:

   • Dark Energy Effective Mass ($M_{de}$) is defined as the effective mass of dark energy that contributes to the gravitational dynamics of a galaxy cluster. Unlike traditional matter, dark energy has a negative effective mass ($M_{de}<0$) due to its repulsive, antigravitational properties. This negative mass affects the total gravitating mass of the cluster.​

2. Mathematical Formulation:

   • The effective mass of dark energy within a spherical volume of radius $R$ is given by: $$M_{de}(R) = \frac{8 \pi}{3} \rho_{de} R^3$$where $\rho_{de}$ is the density of dark energy. For instance, at different radii:
     • At $R = 1.4$ Mpc: $M_{de} = -2.3 \times 10^{12} M_{\odot}$
     • At $R = 4.8$ Mpc: $M_{de}=-9.4\times 10^{13}{M}_{\odot }$
     • At $R = 14$ Mpc: $M_{de} = -2.3 \times 10^{15} M_{\odot}$​

3. Equation for Total Gravitating Mass:

   • The total gravitating mass ($M_g$) within a radius $R$ of a galaxy cluster is the sum of the matter mass ($M_m$) and the dark energy effective mass ($M_{de}$): $$M_g = M_m + M_{de}$$This equation allows us to calculate the total gravitating mass of the cluster by adding the matter mass to the dark energy effective mass. For example, at $R = 14$  Mpc, the total gravitating mass $M_g$ approximates $4.7 \times 10^{15} M_{\odot}$.

4. Implications:

   • The negative effective mass of dark energy implies that, at large distances from the cluster center, the dark energy's repulsive force can exceed the gravitational attraction of the matter within the cluster. This antigravitational effect becomes significant at distances beyond the zero-gravity radius ($R_{zg}$), beyond which the dark energy's influence dominates.

The study by Chernin et al. highlights the substantial impact of dark energy on the structure and mass estimation of galaxy clusters, underscoring its role in shaping cosmic structures and influencing their dynamics.

Exploring a provocative hypothetical scenario where galaxies emerged from gravity rather than from matter:

Soumendra Nath Thakur

11-09-2024

Mr. Martin T. Bosnev's concluding statements explore a provocative hypothetical scenario where galaxies emerged from gravity rather than from matter, fundamentally challenging current cosmological models. In this view, gravity is considered a pre-existing phenomenon, independent of mass and energy, suggesting a reversal in the traditional relationship between matter and gravity. Instead of spacetime being shaped by mass and energy, as posited by general relativity, gravity could independently structure spacetime, shaping the universe at a deeper level. This would imply that galaxies originate from gravitational wells that exist without the presence of matter, with gravity acting as a funnel to channel matter and form galaxies. This conception presents gravity as a primary force not contingent on mass, thereby contradicting the standard model and quantum mechanical interpretations, and suggesting a universe where gravity exists independently from matter, challenging the notion of fundamental entities like particles or matter. Bosnev's hypothesis ultimately calls for a new theoretical framework that integrates gravity, quantum mechanics, and spacetime, potentially replacing general relativity and the Standard Model with a theory where gravity exists autonomously from matter.

Points in view of the description:

1. Galaxies emerged from gravity rather than from matter.

2. Gravitational force is considered a pre-existing phenomenon rather than a result of mass and energy.

3. Spacetime is not shaped by mass and energy.

4. Galaxies originate from gravitational wells independently, with gravity channelling matter through a funnel, creating galaxies.

5. Gravity is presented as a primary force independent of mass, contradicting the standard model and quantum mechanical interpretations.

6. Gravity's existence independent of matter suggests a universe with fundamental forces and fields.

7. A new theory is needed to allow gravity to exist independently of matter, potentially replacing existing theories.

Time: A Concrete Entity in Relativity or an Abstract Concept in Broader Scientific Understanding?

ResearchGate Question Link

By Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

09-09-2024

In human psychology, time is a conscious experience—a construct reflecting the sequence of existence and events. In cosmology and physical sciences, time is often defined as the indefinite, continuous progression of existence and events in a uniform and irreversible succession, extending from the past, through the present, and into the future. This progression is conceptualized as a fourth dimension that exists above the three spatial dimensions.

Time is fundamentally a measurement to quantify changes in material reality. The SI unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also recognized as one of the seven fundamental physical quantities in both the International System of Units (SI) and the International System of Quantities.

In physics, time is commonly defined by its measurement—essentially, "what a clock reads."

This description suggests that time, in its conventional understanding across various scientific disciplines and human experience, is an abstract concept, not a real, tangible entity. While time provides a framework for understanding the succession of events, it does not have a direct physical existence as space does in three dimensions. Time is often viewed as a hyper-dimensional abstraction—imperceptible and unreachable beyond the three-dimensional spatial realm.

However, relativity challenges this interpretation by treating time as a real entity—integrated with space to form a four-dimensional space-time continuum where time becomes subject to physical modifications, such as time dilation. This relativistic concept implies that time is not only concrete but also malleable under the influence of velocity and gravity, leading to discrepancies with other scientific interpretations that consider time an abstract or imaginary concept.

One of the main contentions is that time dilation, a cornerstone of relativity, effectively violates the standardization of time by presenting it as something dilatable, thereby questioning the uniformity and constancy of time itself. The traditional time scale based on a 360-degree cycle—representing a consistent progression—is disrupted by the relativistic notion of time dilation, which converts abstract time into something perceived as "real" or "natural." This treatment of time also seems to ignore the conscious human experience, which understands time as a subjective, psychological construct.

Furthermore, if time is not directly reachable—being an abstract hyper-dimensional concept—what then is the "time" that a clock measures? Clocks are designed to provide a standardized approximation of cosmic time through calibrated frequency counts, such as the electronic transitions of caesium atoms. However, the physical manifestation of time in clocks is inherently subject to distortions, primarily due to gravitational effects. Gravity affects mass and energy, altering the oscillation rates of clocks and resulting in time distortions. Consequently, even the most accurate atomic clocks require periodic adjustments to compensate for these external influences.

The discrepancy between the "real time" measured by clocks and the "conceptual time" of cosmic progression raises further questions about the nature of time. Clocks, intended to represent a uniform progression of time, must contend with gravitational influences that disrupt this uniformity, necessitating ongoing corrections. This challenges the idea that time is a tangible, concrete entity and supports the view that it remains fundamentally an abstract concept—a conceptual framework through which we interpret the order of existence and events.

In short, while relativistic physics proposes that time is a real entity susceptible to physical modifications like time dilation, this interpretation remains contentious when viewed through the lens of broader scientific understanding. Time appears more consistent with an abstract or imaginary concept, a near-approximate representation that is susceptible to external influences, yet ultimately remains beyond the realm of tangible existence.

#Interpretation #Concrete #Conceptualization #Consciousness #AbstractInterpretation #AtomicClock #Time #3Dimensional #dimensionalmeasurementaccuracy