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:

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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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.

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

The extended classical mechanics framework offers a distinctive approach to addressing the issues of singularity and black hole physics, distinguishing itself from traditional relativistic interpretations. In contrast to general relativity, which faces challenges at singularities and is limited in describing physics beyond the Planck scale, extended classical mechanics provides an alternative perspective that incorporates gravitational and kinetic dynamics without the reliance on spacetime curvature.

This framework emphasizes that the universe's total energy is defined by the interplay between potential energy (PE) and kinetic energy (KE), with PE being proportional to dark energy contributions and KE representing motion dynamics. As the potential energy transitions from infinity towards zero and kinetic energy from zero towards infinity, a balanced state emerges, demonstrating that these opposing forces drive the universe's expansion and dynamics. This approach negates the need for traditional singularities, offering a continuous and dynamic model.

Extended classical mechanics explains black hole physics by considering the direct influence of gravitational forces on matter and energy. It proposes that negative effective mass, a concept stemming from gravitational dynamics, plays a crucial role in the motion and interaction of objects within strong gravitational fields, such as those near black holes. The equations governing this framework highlight that gravitational forces impact objects directly, rather than through spacetime distortion, invalidating the need for the singular, infinitely dense points described in conventional black hole models.

Furthermore, this framework bypasses the limitations imposed by the Planck length, which general relativity struggles to address, as it suggests that the extreme conditions near black holes do not necessarily lead to singularities but instead involve complex energy and momentum exchanges. The interaction-driven perspective of extended classical mechanics reinterprets phenomena near black holes, focusing on dynamic mass-energy relationships rather than abstract spacetime curvature.

In summary, extended classical mechanics redefines the understanding of singularity and black hole physics by integrating direct gravitational and kinetic effects, offering a coherent model that goes beyond the constraints of relativistic mechanics and avoiding the problematic infinities associated with traditional singularities.

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

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

Extended classical mechanics offers an alternative framework for understanding the behaviour of gravitational waves, particularly in the context of binary black hole mergers, by focusing on the dynamic interactions of mass and energy rather than relying on spacetime curvature as described by general relativity.

Key Predictions and Insights:

Gravitational Waves as Momentum Exchange: Extended classical mechanics views gravitational waves not as ripples in spacetime but as manifestations of momentum and energy exchanges between massive bodies. In binary black hole mergers, these waves represent the oscillatory exchange of kinetic and potential energy between the interacting masses. This perspective shifts the focus from spacetime distortion to direct interactions governed by the dynamics of the merging bodies.

Effective Mass and Wave Generation:

The theory introduces the concept of effective mass, including both ordinary and apparent (negative) mass components, which influence the generation of gravitational waves. During a merger, the fluctuating effective mass and associated energy dynamics produce waves that propagate as energy disturbances. These waves encode information about the mass distribution, energy exchange rates, and dynamic forces within the merging system.

Amplitude and Frequency Characteristics:

Unlike general relativity, which ties gravitational wave properties directly to spacetime curvature changes, extended classical mechanics predicts that the amplitude and frequency of gravitational waves are closely related to the variations in effective mass and momentum transfer during the merger. As the black holes spiral inward, the increasing rate of energy exchange intensifies the wave amplitude and frequency, culminating in a peak at the point of coalescence.

Energy Conservation in Mergers:

The framework emphasizes conservation laws where the total energy—kinetic and potential—remains consistent even as gravitational waves carry energy away from the system. The merger does not violate energy conservation principles but redistributes energy between the black holes and the emitted gravitational waves, ensuring that total system energy, including radiated waves, aligns with the mechanics of interaction rather than spacetime deformation.

Avoidance of Singularities:

Extended classical mechanics inherently avoids singularity issues by not requiring infinite densities or curvatures. The predicted behaviour of gravitational waves during black hole mergers reflects continuous energy dynamics without the need for spacetime to reach undefined states. This smooth transition in wave production offers a more physically intuitive picture of the merger process.

Implications for Detection:

Gravitational waves detected from binary black hole mergers would still align with the observational data but would be interpreted as energy flows rather than spacetime disturbances. The phase and amplitude evolution of these waves, as observed by detectors like LIGO and Virgo, would still provide insights into the mass, spin, and dynamics of the merging black holes, but through the lens of direct force interactions.

Conclusion:

In the context of binary black hole mergers, extended classical mechanics predicts that gravitational waves are the result of dynamic energy exchanges between interacting masses rather than distortions of spacetime. This approach provides a consistent and alternative interpretation of wave generation, emphasizing momentum transfer and energy conservation, and aligns well with observational evidence without requiring the complex geometrical constructs of general relativity.

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

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