Soumendra Nath Thakur
Tagore's Electronic Lab, India
February 05, 2025
Abstract
Extended Classical Mechanics (ECM) introduces the concept of negative apparent mass, redefining gravitational dynamics and acceleration in a novel framework. Unlike classical mechanics, ECM incorporates apparent mass, which dynamically alters the effective mass of a system. A reduction in apparent mass—especially when negative—leads to an increase in effective acceleration, offering a fresh perspective on cosmic expansion and gravitational interactions.
This framework challenges relativistic spacetime expansion, proposing that the observed accelerated recession of galaxies is a consequence of decreasing effective mass rather than the expansion of space itself. ECM provides an alternative explanation for Hubble’s Law, where galaxy recession velocities increase due to weakened gravitational binding rather than metric expansion. The model also establishes a deep connection between photon dynamics and dark energy, suggesting that both exhibit gravitational effects through apparent mass interactions rather than intrinsic rest mass.
By redefining the role of mass in gravitational equations, ECM aligns with empirical observations, such as those from Chernin et al. (2013) Dark energy and the structure of the Coma cluster of galaxies, and offers a consistent mathematical framework. This directly challenges the traditional reliance on spacetime curvature as the foundation of gravitational interactions and provides a new pathway to understanding cosmic acceleration, dark energy, and the fundamental nature of gravitational forces at interstellar and intergalactic scales.
Newton’s Second Law and Acceleration:
Newton's second law states that force is proportional to mass and acceleration. It implies that if mass increases, acceleration decreases, or if acceleration increases, mass must decrease to maintain the inverse relationship. Classical mechanics does not consider the concept of negative apparent mass, despite some observations suggesting it might be necessary in certain contexts.
Classical Acceleration vs. Effective Acceleration in ECM:
In classical mechanics, acceleration is inversely proportional to mass. However, in Extended Classical Mechanics (ECM), the introduction of apparent mass changes the total mass dynamically, leading to an effective mass. If the apparent mass decreases or becomes negative, the effective mass becomes smaller than the classical mass, leading to an increase in effective acceleration.
Apparent Mass, Effective Mass, and Their Influence on Acceleration in ECM:
In ECM, the effective mass is modified by the presence of apparent mass. This leads to an equation where the force depends on the sum of matter mass and apparent mass. The effective mass changes based on the apparent mass, which influences the acceleration.
Reduction of Apparent Mass and Its Effects:
A decrease in the apparent mass results in an increase in the effective acceleration under constant force. This demonstrates that the acceleration can increase due to the reduction of apparent mass rather than an increase in matter mass.
Effects of Apparent Mass Reduction on Effective Acceleration and Cosmological Dynamics:
The total effective mass in ECM can be influenced by dark energy, which has a negative effective mass. A negative apparent mass reduces the total effective mass, resulting in increased acceleration. This has implications for cosmological models and the understanding of gravitational effects, particularly in the context of dark energy and its role in cosmic expansion.
Extended Classical Mechanics vs. Relativity: A Superior Framework:
The introduction of negative apparent mass in Extended Classical Mechanics (ECM) offers a new perspective on classical mechanics, extending its explanatory power beyond traditional frameworks. This shift provides better insights into gravitational interactions, especially at interstellar and intergalactic scales.
Relativistic mechanics, particularly the use of Lorentz transformations, has limitations because it:
Does not account for classical acceleration effects between rest and moving frames.
Treats the speed of light as the primary defining factor, without considering material stiffness and its role in physical interactions.
ECM addresses these limitations and provides an alternative that challenges certain aspects of relativistic mechanics.
Conclusion:
The introduction of negative apparent mass in ECM leads to a better understanding of force, acceleration, and gravitational interactions, offering a more comprehensive framework compared to relativity.
Effective Mass, Acceleration, and Cosmological Implications in ECM:
ECM offers a framework where effective acceleration is influenced by effective mass. The effective mass is dynamically defined, incorporating both matter mass and dark energy.
The gravitational force equation within ECM accounts for the negative contribution of dark energy, affecting the gravitational dynamics. A decrease in effective mass leads to a reduction in distance for gravitational interactions, leading to higher acceleration when effective mass decreases.
Cosmological Implications of Decreasing Effective Mass:
In cosmology, the reduction of effective mass within gravitational dynamics explains the accelerated recession of galaxies or galactic clusters. This acceleration occurs not because of relativistic space expansion but due to the reduction in effective mass in gravitational interactions.
This interpretation challenges the conventional model of spacetime expansion in relativity, suggesting that galactic recession is the actual cause of observed cosmic dynamics, and not the expansion of space. This calls for a re-evaluation of the current framework of relativistic spacetime expansion.
Hubble’s Law as a Consequence of Decreasing Effective Mass:
In a system where gravitational force remains constant, the observed recession of galaxies and clusters corresponds to an increase in the distance between them over time.
An increase in distance requires a decrease in effective mass, which leads to the accelerated recession of massive bodies with increasing distance.
This phenomenon aligns with Hubble’s Law, which states that the recession velocity of galaxies increases with distance.
The accelerated expansion of the universe is explained by the continuous decrease in effective mass, rather than the relativistic expansion of space itself.
The recession of galaxies is thus a physical effect due to the reduction in effective mass, not an expansion of spacetime, challenging the relativistic interpretation of cosmic expansion.
Cosmological Implications:
The decreasing effective mass provides a logical and empirical foundation for reconsidering gravitational dynamics in cosmology.
This framework offers a mathematical explanation for the observed accelerated recession of galaxies, reinforcing the validity of Extended Classical Mechanics (ECM) as an alternative for understanding cosmic expansion.
Empirical Validation Through Observations:
The approach is supported by Hubble’s Law, which is based on astronomical observations.
Studies, such as the one by Chernin et al. (2013), provide observational backing for the mass-energy interactions described in ECM, lending credibility to the framework.
Mathematical Consistency Across Motion & Gravitation:
The relationship between motion and gravitational dynamics is coherent. As galaxies recede and distance increases, the effective mass decreases, which follows the classical inverse relationship between mass and acceleration.
This mathematical consistency underscores the robustness of ECM as a theoretical framework.
Implications for Cosmic Expansion:
The interpretation suggests that the recession of galaxies is caused by a decrease in effective mass, rather than the relativistic expansion of spacetime.
This challenges a core assumption of modern cosmology and provides an alternative explanation for the observed accelerated recession of galaxies.
Introduction to Extended Classical Mechanics (ECM):
ECM revises the understanding of gravitational dynamics by introducing the concept of effective mass, which accounts for both matter mass and apparent mass.
Apparent mass can take negative values, leading to significant implications for motion and acceleration in gravitational systems.
This framework challenges the conventional relativistic interpretation of cosmic expansion and offers an alternative explanation based on classical mechanics.
Defining Effective Mass in ECM:
In ECM, effective mass includes the matter mass of an object and the contribution from dark energy, which is negative.
If the apparent mass is negative, the effective mass becomes smaller, which increases acceleration under an applied force.
This leads to the inverse relationship between acceleration and effective mass, where a decrease in effective mass increases acceleration.
These principles have important implications for cosmology, particularly for explaining galactic recession without needing relativistic spacetime expansion.
Observations, such as those by Chernin et al. (2013), support the idea that negative apparent mass effects manifest in large-scale gravitational structures.
Reinterpreting Cosmic Expansion Through ECM:
Conventional cosmology attributes the accelerated expansion of the universe to the relativistic expansion of spacetime.
ECM proposes that the observed expansion is instead due to the accelerated recession of galaxies, which is caused by the decreasing effective mass within cosmological gravitational dynamics.
The recession velocity of galaxies is related to their distance through Hubble’s Law, but ECM suggests that this acceleration is due to the continuous decrease of effective mass, not the expansion of space.
As the effective mass decreases, galaxies appear to recede faster with increasing distance, which is explained by the dynamics of mass and acceleration in ECM.
Therefore, the recession of galaxies is a physical effect due to the reduction of effective mass, rather than a result of spacetime expansion.
Mathematical Basis of ECM’s Explanation
The relationship between effective mass and cosmic expansion is established through gravitational interactions.
As effective mass decreases due to the negative contribution of dark energy mass, gravitational binding weakens.
If gravitational force remains constant, the increase in separation between galaxies requires a further decrease in effective mass.
This results in greater acceleration of galaxies, explaining their increasing recession velocities.
Cosmological Implications of Decreasing Effective Mass
The decrease in effective mass provides a fundamental reason for the accelerated recession of galaxies and galactic clusters.
Instead of being caused by relativistic expansion of space, galactic recession results from the reduced gravitational binding due to decreasing effective mass.
This interpretation offers observational evidence supporting effective mass reduction as the actual cause of galactic recession.
It challenges the conventional relativistic model of spacetime expansion, suggesting that the physical motion of galaxies—not space expansion—is the correct explanation of cosmic dynamics.
Photon Motion and Its Equivalence to Dark Energy in ECM
ECM proposes an equivalence between the gravitational behaviour of massless photons and that of dark energy, both arising from apparent mass contributions.
1. Photon Gravitational Interaction:
Photons have energy but no rest mass, yet they interact gravitationally due to their apparent mass.
Their gravitational influence is not from intrinsic mass but from their interaction within gravitational potentials.
2. Dark Energy and Its Negative Effective Mass:
Dark energy contributes to gravitational interactions via apparent mass, similar to photons.
The effective mass of dark energy is negative, influencing large-scale cosmic dynamics.
This suggests that the gravitational effects of dark energy could be interpreted similarly to those of photons but at a cosmic scale.
Implications for Cosmic Expansion and Photon Gravitational Dynamics
In ECM, photons and dark energy influence gravitational interactions through their apparent mass rather than intrinsic rest mass.
Dark energy’s negative effective mass significantly modifies gravitational interactions at intergalactic scales, driving cosmic acceleration.
The equivalence between photon motion and dark energy dynamics suggests that the observed redshift in Hubble’s Law might be linked to the apparent mass effects of light propagation, rather than spacetime expansion.
Conclusion
ECM integrates massless objects into gravitational dynamics and establishes the link between apparent mass, photons, and dark energy.
The acceleration of cosmic expansion is fundamentally tied to decreasing effective mass, challenging the conventional idea of expanding spacetime.
Observational data, such as studies by Chernin et al. (2013), reinforce ECM as a strong alternative framework for explaining cosmic dynamics.
Key Research Insights
Hubble’s Law and Recession Velocity
The recession velocity of galaxies increases with distance, following Hubble’s Law.
This velocity can exceed the speed of light due to cosmic expansion, leading to observable redshift.
Redshift and Photon Energy Loss
As galaxies move apart, photon wavelengths stretch, resulting in cosmological redshift.
This leads to a decrease in photon frequency and energy over large cosmic distances.
Energy Dissipation of Photons
Photons lose energy while traveling through expanding space.
At extreme redshifts, their energy eventually reaches zero, making them undetectable.
This hints the observable universe’s limit at approximately 46 billion light-years.
Cosmic Expansion and Hubble’s Law Consistency
Hubble’s Law remains valid when considering the dynamic separation of galaxies.
Dark energy’s repulsive effect aligns with observations without requiring additional space-stretching mechanisms.
Observable Universe and Horizon
The observable universe is limited by how far light has travelled in 13.8 billion years.
Expansion and photon energy loss contribute to defining this horizon.
Integration into ECM Framework
Comparing ECM Predictions to Hubble’s Law
If ECM attributes galactic recession to decreasing effective mass, its predictions should align with or diverge from Hubble’s Law.
The relationship between recession velocity and redshift could serve as a test for ECM’s validity.
Quantifying Photon Energy Loss in ECM
ECM’s approach to mass and apparent mass could influence photon energy dissipation.
Investigating whether ECM predicts similar energy depletion trends without invoking space expansion would be a valuable test.
Effective Mass and the Horizon
ECM’s alternative explanation for cosmic expansion may offer a different perspective on the universe’s horizon.
Comparing ECM’s predictions of maximum observable distance with current empirical limits could validate its framework.
Extended Classical Mechanics (ECM) and Gravitational Dynamics
The concept of effective mass and its role in gravitational interactions.
How ECM reinterprets the equivalence principle and mass-energy dynamics in gravitational fields.
Dark Energy and Galaxy Cluster Structures
Observational studies on the Coma cluster and its connection to dark energy.
Evidence supporting mass-energy interactions affecting large-scale cosmic structures.
Photon Dynamics and Effective Mass in ECM
The relationship between photons, effective mass, and negative inertia.
How photon interactions exhibit properties analogous to dark energy in ECM.
ECM’s Perspective on Dark Energy
A proposed alternative to the standard ΛCDM model.
How ECM explains cosmic expansion without invoking traditional spacetime stretching.
Photon Energy Interactions and Conservation Laws
A symmetry-based approach to photon energy exchanges in gravitational fields.
How ECM maintains consistency with conservation principles while modifying traditional interpretations.
Hubble Constant and Implications for Cosmology
Empirical studies refining the Hubble constant measurement.
Potential evidence for physics beyond the ΛCDM framework.
Alphabetical List of ECM Terms
• Apparent Mass (Mᵃᵖᵖ) – A dynamic mass term reflecting observed mass variations under external forces, which can become negative due to effective mass contributions.
• Baryonic Mass – The component of matter consisting of protons, neutrons, and electrons, distinguishable from dark matter.
• Cosmological Integration in ECM – The incorporation of empirical cosmological observations and principles, such as dark energy effects at intergalactic scales, into ECM’s gravitational framework.
• Dark Energy (Λ or DE) – A cosmological component influencing the large-scale structure of the universe but having no effect within gravitationally bound systems.
• Dark Matter (DM) – A non-luminous form of matter detectable through gravitational effects, which does not interact with dark energy within gravitational influence but may interact at intergalactic scales.
• Effective Acceleration (aᵉᶠᶠ) – The acceleration influenced by effective mass (Mᵉᶠᶠ) in ECM, distinct from classical acceleration.
• Effective Mass (Mᵉᶠᶠ) – The net mass contributing to gravitational and inertial effects, defined as the difference between matter mass (Mᴍ) and apparent mass (Mᵃᵖᵖ).
• Energy-Frequency Relation – A fundamental equation from Planck's theory, extended in ECM to incorporate refined momentum and mass relations.
• Extended Classical Mechanics (ECM) – A theoretical extension of classical mechanics incorporating negative apparent mass, dark energy, and their effects on motion and gravity.
• Gravitational Potential Energy in ECM – The potential energy formulation incorporating effective mass, distinguishing it from traditional Newtonian gravity.
• Hubble’s Law – The observational relationship between distance and recession velocity of galaxies, more precisely refined in ECM.
• Intergalactic Scale – A scale at which both dark matter and dark energy effects become noticeable, unlike within gravitationally bound systems.
• Lorentz Transformations – Mathematical formulations in relativity that ECM redefines due to their limitations in accounting for acceleration and material stiffness.
• Matter Mass (Mᴍ) – The total mass including both baryonic and dark matter, where dark matter effects become significant at intergalactic scales.
• Momentum in ECM – A refined momentum formulation incorporating effective mass and quantum mechanical principles such as de Broglie’s wavelength relation.
• Negative Apparent Mass (Mᵃᵖᵖ < 0) – A condition where the apparent mass term reduces the observable mass, emerging in high-velocity or strong gravitational field conditions.
• Quantum Mechanical Integration in ECM – The incorporation of principles such as Planck’s and de Broglie’s relations into ECM’s mass and motion framework.
• Refined Newtonian Gravity – A modification of classical gravity within ECM that incorporates effective mass and reinterprets gravitational interactions beyond the Newtonian framework.
Keywords:
Extended Classical Mechanics, ECM, Negative Apparent Mass, Effective Mass, Matter Mass, Dark Energy, Gravitational Dynamics, Acceleration & Force, Newton’s Second Law, Effective Acceleration, Cosmological Implications, Interstellar & Intergalactic Scales, Relativity vs. ECM, Lorentz Transformations, Spacetime Expansion, Hubble’s Law, Galactic Recession, Redshift & Photon Energy Loss, Photon Dynamics, Negative Inertia, Mass-Energy Interactions, Gravitational Binding, Observational Evidence, Cosmic Expansion, Mathematical Consistency in ECM, Alternative to ΛCDM Model, Empirical Validation, Reinterpreting Cosmic Expansion, Energy Dissipation in Photons, Observable Universe Limit, Horizon & Effective Mass, Gravitational Force Equation in ECM, Apparent Mass Effects, Material Stiffness in Physical Interactions, Redefining Gravitational Interactions, Comparison with General Relativity, Recession Velocity & Distance Relation, Hubble Constant Refinement, Gravitational Potential & Photon Motion, Negative Contribution of Dark Energy,
References
1. Thakur, S. N. Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints 2024, 2024091190. https://doi.org/10.20944/preprints202409.1190.v2
2. 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
3. Thakur, S. N. Photon Dynamics in Extended Classical Mechanics: Effective Mass, Negative Inertia, Momentum Exchange and Analogies with Dark Energy. Preprints 2024, 2024111797. https://doi.org/10.20944/preprints202411.1797.v1
4. Thakur, S. N. A Nuanced Perspective on Dark Energy: Extended Classical Mechanics. Preprints 2024, 2024112325. https://doi.org/10.20944/preprints202411.2325.v1
5. Thakur, S. N. A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields. Preprints 2024, 2024110956. https://doi.org/10.20944/preprints202411.0956.v1
5. Riess, A. G., et al. (2019). Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM. The Astrophysical Journal, 876(1), 85. DOI: https://doi.org/10.3847/1538-4357/ab1422
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