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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8. Can the framework explain the observed baryon acoustic oscillations (BAOs) in the large-scale structure of the universe?

The extended classical mechanics framework offers a unique perspective on baryon acoustic oscillations (BAOs) by emphasizing the interactions of mass and energy within the universe rather than relying solely on general relativity's treatment of spacetime. Here's how this framework can explain the observed BAOs:

Key Explanations:

Sound Waves in the Early Universe: BAOs are generated from sound waves that propagated through the hot, dense plasma of baryonic matter and radiation in the early universe. Extended classical mechanics can model these oscillations as the result of pressure and gravitational interactions between baryons and photons. As the universe expanded and cooled, these sound waves left imprints on the distribution of matter, leading to characteristic density fluctuations.

Energy Transfer Mechanism:

The framework posits that these oscillations arise from the dynamic energy exchanges between baryons and the radiation field. When baryons experience gravitational attraction, they oscillate around their equilibrium positions, creating pressure waves. This energy transfer during these oscillations is integral to understanding how BAOs manifest in the cosmic microwave background (CMB) and large-scale structures.

Effective Mass Considerations:

In this context, the concept of effective mass plays a crucial role. The baryonic mass is influenced by both ordinary and apparent (negative) mass components, which can affect the dynamics of oscillations. The interplay between these masses governs how energy is distributed throughout the oscillating medium, shaping the resulting structures in the universe.

Formation of Large-Scale Structures:

As the universe expands, these oscillations contribute to the formation of large-scale structures, such as galaxy clusters. The regions of higher density resulting from BAOs lead to gravitational attraction that drives the clustering of matter. This clustering can be analysed through the framework's emphasis on energy conservation and momentum exchange, providing insights into the distribution of galaxies and cosmic structures.

Avoiding Singularities:

Extended classical mechanics sidesteps the singularity issues that arise in traditional models. By focusing on dynamic interactions and energy flow, it offers a more continuous framework for understanding the evolution of structures influenced by BAOs, without invoking undefined states or infinities.

Alignment with Observations:

The predictions of this framework regarding the scale of BAOs align with observational data from the CMB and galaxy surveys. The periodicity seen in galaxy distributions can be interpreted as the result of the coherent oscillations that originated in the early universe, reflecting the underlying dynamics of mass interactions.

Conclusion:

In summary, the extended classical mechanics framework can effectively explain baryon acoustic oscillations by modelling them as dynamic interactions of mass and energy in the early universe. By focusing on sound waves, effective mass considerations, and energy transfer mechanisms, this approach provides a coherent understanding of how BAOs influence the large-scale structure of the universe while avoiding the complications associated with singularities in traditional models.

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9. How does extended classical mechanics address the cosmological horizon problem?

Extended classical mechanics offers an alternative approach to addressing the cosmological horizon problem by focusing on the dynamics of mass and energy interactions rather than relying solely on the traditional models of inflation or cosmic expansion. Here are some key points on how this framework addresses the issue:

Key Explanations:

Dynamic Mass Interactions: The extended classical mechanics framework emphasizes the interactions between ordinary matter, dark matter, and energy, proposing that these dynamics influence the propagation of information and signals across the universe. By considering how these interactions shape the evolution of the cosmos, the framework provides a basis for understanding how regions of space that appear causally disconnected may still exhibit similar properties.

Effective Mass and Gravitational Effects:

The concept of effective mass, including both ordinary and apparent (negative) mass components, plays a crucial role in explaining how gravitational effects can reach across large distances. This perspective suggests that the gravitational influence of matter can extend beyond conventional horizons, allowing for correlations in temperature and density across vast scales.

Energy Conservation in Expanding Space:

In this framework, energy conservation remains central, even as the universe expands. The interplay between gravitational potential energy and kinetic energy contributes to the overall dynamics, enabling the transmission of information across regions that, according to standard models, should be causally disconnected. This continuity can help explain the uniformity observed in the cosmic microwave background (CMB).

Baryonic Acoustic Oscillations and Homogeneity:

By incorporating the dynamics of baryon acoustic oscillations, the framework accounts for the observed homogeneity and isotropy of the universe on large scales. These oscillations, which propagate through the early universe, create density fluctuations that influence large-scale structure formation, contributing to the apparent uniformity across the cosmological horizon.

Avoidance of Singularities:

Unlike traditional models that may encounter singularities or undefined states, extended classical mechanics provides a continuous framework for understanding cosmological evolution. This avoids issues related to horizon limits, as the dynamics of mass and energy interactions remain consistent throughout the universe's expansion.

Implications for Observational Cosmology:

The framework's predictions align with observations of the CMB and the large-scale structure of the universe. By examining how effective mass and gravitational interactions shape the cosmic landscape, the framework offers insights into the horizon problem without invoking the complexities of inflationary models.

Conclusion:

In summary, extended classical mechanics addresses the cosmological horizon problem by focusing on the dynamic interactions of mass and energy throughout the universe. By emphasizing effective mass, energy conservation, and the role of gravitational influences, this approach provides a coherent understanding of how causally disconnected regions can exhibit uniform properties, ultimately offering a new perspective on cosmic evolution and structure formation.

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10. How does extended classical mechanics predict the behavior of cosmological perturbations and their impact on structure formation?

Extended classical mechanics provides a unique framework for understanding cosmological perturbations and their role in structure formation by emphasizing the dynamics of mass-energy interactions and effective mass concepts. Here’s how this framework predicts the behaviour of cosmological perturbations:

Key Predictions and Insights:

Perturbation Dynamics: Extended classical mechanics treats cosmological perturbations as variations in the distribution and motion of matter and energy within the universe. By considering these perturbations as oscillatory patterns in the effective mass, the framework predicts how small density fluctuations evolve over time, influencing large-scale structure formation.

Effective Mass Concept:

The concept of effective mass, which includes ordinary mass, dark matter mass, and apparent mass, plays a critical role in determining how gravitational interactions propagate through the universe. Perturbations in the effective mass influence gravitational fields, leading to the growth or decay of density fluctuations. This results in the clumping of matter and the formation of structures like galaxies and clusters.

Gravitational Collapse:

The framework predicts that perturbations with sufficient amplitude will undergo gravitational collapse, leading to the formation of structures. As these perturbations evolve, regions with higher effective mass attract surrounding matter, leading to the growth of cosmic structures over time. This process aligns with observations of galaxy formation and clustering in the universe.

Energy Conservation and Oscillations:

The extended classical mechanics framework maintains that energy conservation is fundamental to the evolution of cosmological perturbations. Oscillations in density due to baryonic acoustic oscillations (BAOs) provide a mechanism for understanding how these perturbations impact structure formation, allowing for the transfer of energy between kinetic and potential forms as structures evolve.

Impact of Dark Energy:

The role of dark energy and its influence on effective mass dynamics is also considered. As the universe expands, dark energy contributes to the overall energy balance, affecting how perturbations grow or decay. The framework predicts that the interplay between dark energy and gravitational interactions modifies the growth rates of structures, offering insights into observed phenomena such as accelerated expansion.

Mathematical Formulation:

Extended classical mechanics provides mathematical tools to describe the evolution of perturbations. By employing equations that incorporate effective mass, gravitational forces, and energy dynamics, the framework predicts how these perturbations manifest at different scales and evolve into the large-scale structure we observe today.

Conclusion:

In summary, extended classical mechanics predicts the behaviour of cosmological perturbations by focusing on the dynamics of effective mass and gravitational interactions. This framework explains how perturbations evolve, leading to the formation of structures in the universe, while also accounting for the roles of dark energy and energy conservation. By offering a cohesive understanding of these processes, extended classical mechanics provides valuable insights into the fundamental nature of cosmic structure formation.

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