Conceptual Alignment of Apparent Mass and Dark Energy Effective Mass in Gravitational Dynamics: Extended Classical Mechanics.

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

22-09-2024

This presentation explores the interconnected concepts of Negative Effective Mass, highlighting how both Apparent Mass (−Mᵃᵖᵖ) and Dark Energy Effective Mass (Mᴅᴇ) exert negative influences on gravitational dynamics. It emphasizes that these negative mass properties contribute to repulsive forces that counteract gravitational attraction. The relationship between Apparent Mass and total gravitating mass (Mɢ) is established, paralleling the framework proposed by Chernin et al., where Mɢ is derived from the sum of matter mass and dark energy effective mass. The significance of these concepts is particularly pronounced under extreme conditions, such as high velocities and strong gravitational fields, underscoring their importance in cosmic dynamics. Ultimately, the discussion illustrates how Apparent Mass and Dark Energy Effective Mass are conceptually aligned, both playing pivotal roles in shaping gravitational behaviours within galaxy clusters.

1. Negative Effective Mass: 

Both the Apparent Mass (−Mᵃᵖᵖ) and the Dark Energy Effective Mass (Mᴅᴇ) are characterized as having a negative influence on gravitational dynamics. This is central to both concepts, where negative mass contributes to repulsive forces that counteract gravitational attraction.

2. Influence on Gravitating Mass: 

The response emphasizes how Apparent Mass affects the total gravitating mass (Mɢ), showing that it can be expressed as Mɢ = Mᴍ + (−Mᵃᵖᵖ). This is similar to the framework from Chernin et al., where the total gravitating mass is also derived from the combination of matter mass and the dark energy effective mass: Mɢ = Mᴍ + Mᴅᴇ.

3. Context of High Velocities and Strong Fields: 

Both descriptions note that the effects of these negative mass concepts become significant under extreme conditions, such as high velocities or strong gravitational fields, reinforcing the idea that they are crucial for understanding cosmic dynamics.

4. Role in Gravitational Dynamics: 

The alignment is further supported by stating that dark energy’s negative mass plays a significant role in local gravitational dynamics within galaxy clusters, mirroring the implications of Apparent Mass in altering expected gravitational behaviours.

Overall, the presentation conveys that Apparent Mass and Dark Energy Effective Mass share a conceptual foundation, both influencing gravitational dynamics through their negative mass properties.

Keywords: Apparent Mass, Dark Energy, Gravitational Dynamics,

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

#ApparentMass, #DarkEnergy, #GravitationalDynamics,

The Cosmological Constant: A Misaligned Solution for Dark Energy and the Static Universe

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

22-09-2024

The cosmological constant, first introduced by Albert Einstein in 1917, was originally intended to maintain a static model of the universe—one that did not expand or contract. This introduction was a response to the prevailing belief that the universe was unchanging, as no observational evidence of expansion existed at the time. However, subsequent discoveries radically altered this view, revealing an expanding universe driven not by a static equilibrium but by dynamic, evolving forces. As such, the cosmological constant, rather than providing answers to the mysteries of dark energy, primarily served to save Einstein's static universe from gravitational collapse, exposing its misalignment with the nature of an expanding cosmos.

The Genesis of the Cosmological Constant

In 1917, Einstein proposed the "Einstein static universe" model, also known as the Einstein universe or the Einstein static eternal universe, within the framework of General Relativity. This model was based on the assumption that the universe was static and unchanging, a perspective supported by the observational limitations of the time. To uphold this static nature, Einstein realized that gravity alone would cause the universe to collapse due to its self-attracting nature. To counteract this effect, he introduced the cosmological constant (Λ), a repulsive force designed specifically to balance gravitational attraction and maintain the universe's static state.

Einstein's adjustment was detailed in his paper, "The Cosmological Considerations in the General Theory of Relativity," where the cosmological constant was mathematically incorporated into his field equations to provide a stable, non-expanding universe. This solution, however, was more of a mathematical fix than a physical insight into the workings of the cosmos.

The Decline of the Static Universe Model

The concept of a static universe began to crumble when astrophysicist Georges Lemaître and others proposed that the universe was not static but expanding. This revolutionary idea was later confirmed by Edwin Hubble's observations in the late 1920s, which showed that galaxies were receding from each other, signalling an expanding universe. Faced with the reality of cosmic expansion, Einstein famously discarded the cosmological constant, calling it his "greatest blunder." He recognized that the static model was fundamentally flawed and that the universe was not in equilibrium as previously thought.

Cosmological Constant vs. Dark Energy

Despite its origin as a corrective measure for a static universe, the cosmological constant has often been repurposed in modern cosmology as a candidate for dark energy, the mysterious force driving the accelerated expansion of the universe. However, this reinterpretation of the cosmological constant as an explanation for dark energy is fundamentally inconsistent with its original purpose and physical meaning.

The cosmological constant was designed to provide a repulsive force to counteract gravitational attraction, thereby maintaining a static universe—not to explain an expanding one. Even if viewed as a force opposing gravitational collapse, it was not intended to account for an accelerating expansion. Instead, the concept of dark energy encompasses a range of potential mechanisms that influence cosmic acceleration, none of which align directly with the simple, uniform repulsion implied by the cosmological constant.

Dark Energy as a Dynamic Force

Current understanding suggests that the accelerating expansion of the universe arises not from any specific substance or constant repulsive force but from complex gravitational and kinetic interactions within the cosmic fabric. These interactions collectively define what we term as dark energy—a placeholder for the unknown drivers of this expansion. Unlike the static repulsion of the cosmological constant, dark energy is dynamic, evolving with the universe in ways that remain the subject of ongoing research.

In conclusion, while the cosmological constant historically played a role in preserving the notion of a static universe, it does not adequately address the complexities of dark energy in an expanding universe. Instead, it serves as a historical footnote—a reflection of a time when the cosmos was misunderstood as a fixed entity rather than the dynamic and ever-evolving universe we observe today. Thus, the cosmological constant is better seen as a relic of an obsolete model rather than a solution to the profound mysteries of dark energy.

Keywords: Cosmological Constant, Static Universe, Dark Energy, Expanding Universe, Gravitational Collapse,

#CosmologicalConstant, #StaticUniverse, #DarkEnergy, #ExpandingUniverse, #GravitationalCollapse,