Researcher ORCiD: 0000-0003-1871-7803

23 September 2024

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constant to account for dark energy misunderstands its purpose and history, highlighting its abandonment as a relic of outdated cosmological thought rather than a viable explanation for contemporary observations.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.

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

Extended classical mechanics accommodates the observed isotropy (uniformity in all directions) and homogeneity (uniformity in composition) of the universe on large scales by incorporating the concepts of mass-energy dynamics, gravitational influences, and effective mass contributions that are consistent across vast spatial regions. In this framework, the distribution of ordinary mass, dark matter, and the effects of apparent (or effective) mass are considered as key contributors to the universe's large-scale structure.

The isotropy and homogeneity are maintained through a balanced interplay between gravitational forces and the negative effective mass contributions, which help stabilize large-scale cosmic structures without favouring any specific direction or location. This approach aligns with the cosmological principle, which asserts that the universe appears the same everywhere on a large scale. By addressing the cumulative effects of various mass components, extended classical mechanics provides a coherent explanation for the uniformity observed in the cosmic microwave background, galaxy distributions, and large-scale structures, ensuring that the universe's behaviour remains consistent with isotropic and homogeneous characteristics.

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

The concept of negative effective mass within the extended classical mechanics framework offers a novel approach to explaining specific astrophysical phenomena, such as galaxy rotation curves and gravitational lensing. Traditional models, including dark matter theories, often rely on the presence of unseen mass to account for the anomalous rotation speeds of galaxies and the bending of light around massive objects. In contrast, the negative effective mass concept attributes these effects to momentum exchanges and the dynamic interactions of gravitational fields, rather than purely intrinsic spacetime curvature.

For galaxy rotation curves, the effective mass acts as a counterbalancing influence that modifies the observed rotational dynamics without requiring vast amounts of unseen matter. This approach aligns with observed deviations in rotation velocities and provides an alternative explanation for the flat rotation curves seen in galaxies, suggesting that gravitational dynamics are influenced by both the visible and effective mass components.

In the case of gravitational lensing, the bending of photon paths is understood as a result of direct momentum exchange between photons and gravitational fields rather than being purely a manifestation of spacetime curvature. This framework maintains that photons experience changes in momentum and wavelength due to gravitational interactions, preserving their intrinsic energy. The negative effective mass plays a crucial role in this interaction, influencing the observed lensing effect without necessitating a separate dark matter explanation.

Overall, the negative effective mass concept challenges conventional gravitational theories by offering a dynamic, interaction-based perspective on astrophysical phenomena, potentially reshaping our understanding of mass, gravity, and the cosmos.

The phase shift in the oscillation frequency can be used to calculate the magnitude of this time distortion using the following formula:

• For a 1° phase shift: T(deg) = (1/f)/360 = Δt or,
• For an x° phase shift: Δtₓ = x(1/360f₀)

References:

1. 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
2. Thakur, S. N. (2024). Direct Influence of Gravitational Field on Object Motion invalidates Spacetime Distortion. Qeios (ResearchGate). https://doi.org/10.32388/bfmiau
3. Thakur, S. N. (2023). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature. Definitions. https://doi.org/10.32388/81iiae
4. Thakur, S. N., Samal, P., & Bhattacharjee, D. (2023b). Relativistic effects on phaseshift in frequencies invalidate time dilation II. TechRxiv (ResearchGate). https://doi.org/10.36227/techrxiv.22492066.v2
5. Thakur, S. N., & Bhattacharjee, D. (2023). Phase Shift and Infinitesimal Wave Energy Loss Equations. Preprints.Org (MDPI). https://doi.org/10.20944/preprints202309.1831.v1

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