Soumendra Nath Thakur
September 10, 2025
Abstract:
This paper explores the concept of variable matter mass within the framework of Extended Classical Mechanics (ECM), where mass is defined as a frequency-dependent, energy-related property that evolves through interactions, oscillations, and energy exchange processes. Unlike traditional physics, which treats mass as an invariant quantity, ECM proposes that matter mass (Mᴍ) is dynamically shaped by frequency–time distortions, energy density structures (ρᴇ), and the interplay of apparent and effective mass components. The transformative nature of matter mass allows primordial energy to turn into mass and, conversely, mass back into energy—a process deeply influenced by dark energy’s negative effective mass. As dark energy’s role grows, it causes fluctuations in Mᴍ, reducing or even inverting mass, and enabling energy to redistribute across cosmic scales. Observational studies on dark energy’s effects in galaxy clusters, alongside ECM’s theoretical framework, support this view of mass as an emergent, adaptable property rather than a rigid constant[1]. By focusing on how frequency governs these distortions, ECM offers a coherent explanation for how oscillatory energy processes drive the evolution of the universe—stretching its energy density and guiding the constant transformation between mass and energy.
Keywords
Variable Matter Mass; Frequency–Time Distortions; Negative Apparent Mass; Dark Energy; Energy Density Structures; Extended Classical Mechanics (ECM); Emergent Mass; Cyclic Cosmology,
ORCiD: 0000-0003-1871-7803 | Tagore's Electronic Lab, India | postmasterenator@gmail.com
In Extended Classical Mechanics (ECM), matter mass (Mᴍ) is defined as a frequency-dependent, energy-related property of matter that varies with interactions, oscillations, and energy exchange processes rather than being an absolute or static quantity. Unlike the traditional view where mass is treated as an invariant parameter, ECM recognizes that matter’s mass arises from underlying oscillatory behaviours and energy transitions governed by frequency-related phenomena.
This perspective emphasizes that mass is not a rigid attribute but a dynamic result of how matter interacts with energy fields and time-dependent processes. As such, Mᴍ evolves based on the particle’s state, energy density structures (ρᴇ), and time–frequency distortions (Δt, Δf). This frequency-governed nature of mass allows ECM to bridge quantum interactions and macroscopic behaviours within a unified framework, offering a deeper understanding of how energy and matter are interconnected across scales.
Observational evidence such as the study “Dark energy and the structure of the Coma cluster of galaxies” by A. D. Chernin et al. DOI: https://doi.org/10.1051/0004-6361/201220781 supports the existence of negative effective mass associated with dark energy, reinforcing the ECM view that energy interactions at cosmic scales influence gravitational behaviours[1].
Further validation and explanation of ECM’s variable matter mass are provided by the interactive webpage titled “A New Vision of the Cosmos.” URL: http://www.telitnetwork.itgo.com/ExtendedClassicalMechanics/Cosmos/, which offers a narrative guide to the ECM framework[3]. This resource introduces the four key mass components central to ECM—Matter Mass (Mᴍ), Dark Energy Mass (Mᴅᴇ), Effective Gravitational Mass (Mɢ), and Apparent Mass (Mᵃᵖᵖ < 0)—and visually explains how their interactions lead to dynamic changes in cosmic evolution. The webpage’s structured explanation of ECM’s core concepts and cosmic timeline reinforces how matter mass is inherently linked to energy densities and oscillatory processes rather than fixed quantities.
The theoretical foundations provided in the ECM papers “Extended Classical Mechanics (ECM): A Post-Relativistic Interpretation of Early Universe Phenomena and Cosmic Expansion.” DOI: https://doi.org/10.13140/RG.2.2.28556.42888 and “The Self-Triggered Big Bang: ECM’s Internal Mass-Energy Dynamics and the Reinterpretation of Gravitational Origin” DOI: https://doi.org/10.13140/RG.2.2.25903.04003 provide further support, explaining how mass-energy interactions drive early universe dynamics and how gravitational effects emerge from frequency-dependent transitions within matter[4,5]. These works form the deeper mathematical and conceptual basis for ECM’s variable matter mass framework, bridging theoretical constructs with cosmological phenomena.
ECM Kinetic Energy for Dynamic Particles
ECM provides a novel approach to describing the kinetic energy of both massless and massive particles by incorporating effective mass (Mᵉᶠᶠ) and apparent mass (Mᵃᵖᵖ), both of which arise from frequency-dependent interactions.
For Massless or Near-Massless Particles (Photon, Gamma Ray)
In conventional physics, photons are considered massless, with their energy described through relativistic relationships. ECM, however, explains the energy of photons by attributing an apparent mass component linked to frequency transitions.
The kinetic energy is defined as:
KEᴇᴄᴍ = ½Mᵉᶠᶠv²,
where the effective mass is:
Mᵉᶠᶠ = -Mᵃᵖᵖ - Mᵃᵖᵖ = -2Mᵃᵖᵖ,
and v = c, the speed of light for photons or gamma rays.
Substituting into the equation yields:
KEᴇᴄᴍ = ½(-2Mᵃᵖᵖ)c² = Mᵃᵖᵖc².
With Mᵃᵖᵖ = ∆Mᴍ, the change in matter mass due to energy transitions, this simplifies to:
KEᴇᴄᴍ = ∆Mᴍ c² = Mᴍ c²,
showing that the kinetic energy of a photon can be fully explained as a frequency-dependent mass-energy relation in ECM, without requiring relativistic mass adjustments.
For Massive Particles (Electron and Similar Particles)
For particles with inertial mass, ECM expresses the matter mass as a sum of frequency-dependent contributions:
Mᴍ = ∆Mᴍᵈᴮ + ∆Mᴍᴾ,
where:
• ∆Mᴍᵈᴮ corresponds to de Broglie frequency oscillations,
• ∆Mᴍᴾ corresponds to Planck-scale energy interactions.
• f = fᵈᴮ + fᴾ denotes the total effective frequency.
The kinetic energy is then given by:
KEᴇᴄᴍ = (∆Mᴍᵈᴮ + ∆Mᴍᴾ) c²,
illustrating that matter mass is not fixed but evolves with oscillatory interactions and energy density changes across scales.
The Frequency-Dependent Nature of Mass in ECM
A central emphasis of ECM is that mass (Mᴍ) is not an inherent or immutable property but emerges from the underlying structure of energy interactions governed by frequency. Matter’s mass fluctuates based on how particles oscillate, exchange energy, and experience time–frequency distortions in their environment.
This stands in contrast to classical and relativistic physics, where mass is considered constant except in extreme conditions. ECM’s approach integrates micro-level quantum behaviours with macro-level phenomena, offering a unified view that accounts for variations in mass as a natural consequence of energy transitions and frequency interactions.
Observational studies of cosmic expansion, gravitational lensing, and cluster dynamics increasingly suggest anomalies that are consistent with ECM’s dynamic mass framework. The effective negative mass attributed to dark energy, as noted in galaxy cluster observations, provides empirical support for ECM’s prediction that energy interactions can reduce or invert matter mass at large scales[1].
The conceptual foundations of ECM’s dynamic mass framework bear striking parallels to cyclic universe theories, particularly Roger Penrose’s Conformal Cyclic Cosmology (CCC). CCC posits that the universe undergoes endless cycles, or “eons,” where the final phase of one cosmic era—dominated by radiation and lacking conventional mass—smoothly transitions into the Big Bang of the next. ECM’s treatment of mass as a frequency-dependent, emergent property governed by energetic distortions offers a concrete mechanism that aligns with CCC’s theoretical vision. The reversible transformation between dark energy, dark matter, and ordinary matter in ECM mirrors CCC’s cyclical progression, wherein massless states evolve into matter-dominated structures and back again without singularities. Observations of large-scale anomalies in the cosmic microwave background, as referenced in CCC discussions, further resonate with ECM’s predictions about fluctuating matter mass and anti-gravitational influences driven by negative apparent mass[2]. Together, ECM and CCC provide a unified narrative—rooted in frequency-phase dynamics and energy conservation—that explains how the universe perpetually renews itself across cosmic epochs.
The interactive explanations provided by the “A New Vision of the Cosmos” webpage further support this interpretation, illustrating how changes in apparent mass (Mᵃᵖᵖ) influence matter mass (Mᴍ) and drive cosmic evolution[3]. By demonstrating the interplay between Mᴍ, Mᴅᴇ, Mɢ, and Mᵃᵖᵖ, the webpage reinforces the view that mass is fundamentally governed by energy oscillations rather than being a static property.
Additionally, ECM’s theoretical works in “Extended Classical Mechanics (ECM): A Post-Relativistic Interpretation of Early Universe Phenomena and Cosmic Expansion” and “The Self-Triggered Big Bang: ECM’s Internal Mass-Energy Dynamics and the Reinterpretation of Gravitational Origin” provide rigorous mathematical formulations describing how mass-energy interactions evolve and influence cosmic events. These contributions lend robust support to the model's explanation of mass variability[4,5].
How Increasing Negative Apparent Mass Drives Dynamic Mass Changes
ECM’s effective mass equation,
Mᵉᶠᶠ = Mɢ = Mᴍ − Mᵃᵖᵖ,
reveals how interactions influence the energy structure of matter. As the negative component −Mᵃᵖᵖ increases, it directly leads to a decrease in the corresponding matter mass Mᴍ. When this negative influence becomes dominant, it can not only reduce matter mass but also alter the polarity of both the effective mass and the gravitating mass (Mᵉᶠᶠ = Mɢ). This dynamic shift highlights how mass is not fixed but energetically responsive to interactions and oscillations.
In extreme cases, as −Mᵃᵖᵖ grows larger than Mᴍ, the total effective mass can transition from positive to negative, giving rise to anti-gravitational effects and accelerated expansion phenomena such as those attributed to dark energy. Observational evidence from galaxy cluster dynamics and large-scale cosmic expansion corroborates this behaviour, lending credibility to ECM’s prediction that matter mass can energetically change in dynamism rather than remain constant.
The “A New Vision of the Cosmos” guide further illustrates how the balance between Mᴍ and Mᴅᴇ shifts over cosmic time, supporting the idea that increasing dark energy influences the reduction and eventual inversion of matter mass, providing a detailed narrative explanation aligned with ECM’s mathematical framework[3].
Conclusion
Extended Classical Mechanics (ECM) provides a transformative perspective on matter mass, redefining it as a frequency-dependent, energy-related property that evolves through oscillations, interactions, and energy distortions rather than being an inherent or static attribute. By explaining how increasing negative apparent mass reduces matter mass and can even invert its polarity, ECM offers a unified framework that integrates quantum behaviours with cosmic-scale phenomena.
Observational studies—particularly those concerning dark energy’s effects on galaxy clusters and large-scale cosmic expansion—support ECM’s dynamic mass model, offering empirical grounding for its predictions[1]. The interactive explanations on the “A New Vision of the Cosmos” webpage further enhance conceptual clarity by illustrating how variations in apparent mass influence matter mass and gravitational interactions across cosmic timescales[3].
Importantly, ECM’s treatment of mass resonates with cyclic universe theories, such as Roger Penrose’s Conformal Cyclic Cosmology (CCC), which envisions endless cosmic cycles where massless states transition into matter-dominated eras and back again[2]. ECM’s frequency-driven mechanisms offer a concrete energetic explanation for such transitions, linking dark energy’s negative apparent mass to accelerated expansion and matter transformations in ways consistent with observational anomalies like those seen in the cosmic microwave background.
Through this lens, mass emerges as a fluid and adaptable feature—one that reflects the evolving structure of energy and time rather than a rigid, unchanging constant. This conceptual shift not only deepens our understanding of particle kinetics and gravitational dynamics but also offers profound insights into the broader evolution of the universe. By bridging microscopic oscillations with cosmic phenomena and aligning with cyclic cosmological models, ECM presents a coherent, mathematically supported narrative that advances both theoretical physics and our understanding of the universe’s past, present, and future.
References
1. A. D. Chernin, et al., “Dark energy and the structure of the Coma cluster of galaxies,” Astronomy & Astrophysics, 2012. DOI: https://doi.org/10.1051/0004-6361/201220781
2. The Physics of Conformal Cyclic Cosmology. (2025). Krzysztof A. Meissner, Roger Penrose DOI: https://doi.org/10.48550/arXiv.2503.24263
3. “A New Vision of the Cosmos,” Extended Classical Mechanics (ECM), Telit Network. URL: http://www.telitnetwork.itgo.com/ExtendedClassicalMechanics/Cosmos/
4. S. N. Thakur, “Extended Classical Mechanics (ECM): A Post-Relativistic Interpretation of Early Universe Phenomena and Cosmic Expansion,” 2025. DOI: https://doi.org/10.13140/RG.2.2.28556.42888
5. S. N. Thakur, “The Self-Triggered Big Bang: ECM’s Internal Mass-Energy Dynamics and the Reinterpretation of Gravitational Origin,” 2025. DOI: https://doi.org/10.13140/RG.2.2.25903.04003
6. S. N. Thakur, “A Comparative Framework for Extended Classical Mechanics’ Frequency-Governed Kinetic Energy,” (2025). DOI: https://doi.org/10.20944/preprints202508.1031.v1
7. Appendix 30: Post-Latent Energetic Dynamics and the Dual-State Evolution of the Universe in ECM. DOI: https://doi.org/10.13140/RG.2.2.19281.44647
8. Appendix 43: Origin and Fundamental Energy in Extended Classical Mechanics (ECM). DOI: https://doi.org/10.13140/RG.2.2.14836.46725
No comments:
Post a Comment