Clarifying ECM's Stance on Negative Mass and Dark Matter Interactions:

February 11, 2025                                                 RG Discussion Link

Dear Mr. Ian Clague,

Thank you for your response and for referencing J. S. Farnes’ "A Unifying Theory of Dark Energy and Dark Matter." However, your comment appears to operate under assumptions that do not align with the framework and specific content of ECM as presented in this discussion.

1. Irrelevance of External Assertions
   Your comment does not directly address or engage with the ECM framework outlined in this discussion but instead refers to an external model, suggesting an alternative premise without evaluating ECM’s treatment of the subject matter. While referencing other works can be useful in comparative discussions, an assertion such as “Negative mass can explain Dark Matter” without any engagement with the ECM-specific perspective does not constitute a meaningful counterpoint.

2. Misalignment with ECM's Dark Matter Interpretation
   Your statement that "Negative mass can explain Dark Matter as the interaction of negative mass with positive mass" does not apply to ECM, which treats dark matter as possessing positive effective mass. ECM presents dark matter as a contributing component to the total positive matter mass of a system, alongside baryonic matter. The claim that dark matter must be explained via negative mass is inconsistent with ECM’s construct, which does not require negative mass to account for dark matter effects.

3. ECM’s Treatment of Negative Mass vs. Your Assertion
   In ECM, negative apparent mass (−Mᵃᵖᵖ) arises as a motion-dependent or gravitationally induced property, rather than as an intrinsic mass entity. The framework does not support the notion of self-existing, freely interacting negative mass, as assumed in your reference. This distinction is critical because ECM does not describe dark matter in terms of negative mass, contrary to your assertion that "Negative mass can explain Dark Matter."

4. ECM’s Explanation of Dark Energy vs. Your Interpretation
   Your assertion that "Dark Energy [is] the interaction of negative mass and negative mass" contradicts ECM’s position. ECM interprets dark energy as possessing negative effective mass that interacts with the total positive effective mass of ordinary and dark matter. In ECM, dark energy does not arise from negative mass interacting with itself but rather from its interaction with an overall positive matter mass distribution.

Conclusion

Your statements regarding negative mass as the explanation for dark matter and dark energy do not align with ECM’s theoretical structure. The presentation of ECM explicitly defines dark matter as a positive-mass entity and describes dark energy as having a negative effective mass interacting with positive effective mass—not through the interaction of two negative masses, as you claim.

While alternative models, such as Farnes’ theory, exist, an assertion that they necessarily override ECM’s conclusions would require a rigorous comparative analysis rather than an unqualified statement. As such, your assertions are not consistent with ECM’s framework, nor do they provide a valid refutation of its premises.

Best regards,

Soumendra Nath Thakur

My Answers on the Questions about ECM: Dark Energy and Gravitational Potential Energy in ECM.

 RG Discussion Link Here:

February 11, 2025

Dear Mohammad Shafiq Khan,

Thank you for your engagement in the discussion on Extended Classical Mechanics (ECM). I appreciate your thought-provoking questions, and I fully agree that questioning everything is the essence of scientific progress. However, as I am actively engaged in multiple aspects of my research, some responses may take time, as I prefer to provide well-founded answers rather than instant ones.

1. Gravitational Potential Energy in ECM

Within ECM, the gravitational potential energy for a test matter mass mₘ is expressed as:

Uᴇᴄᴍ = − GMᵉᶠᶠmₘ/r 

where: 

• Uᴇᴄᴍ: is the gravitational potential energy of the test mass mₘ
• G: is the gravitational constant
• Mᵉᶠᶠ: is the effective mass of the source
• mₘ: is a test matter mass of the source
• r: is the radial distance

The effective mass Mᵉᶠᶠ accounts for both baryonic matter and the apparent mass contribution, which extends the classical framework to accommodate additional effects such as dark matter and dark energy.

2. Dark Energy in ECM

Dark energy is treated in ECM through the concept of apparent mass (Mᵃᵖᵖ), leading to an effective mass representation:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mɢ

where:

• Mɢ: Gravitating Mass
• Mᴍ: Matter Mass
• −Mᵃᵖᵖ: represents the influence of dark energy (with a negative contribution).

This formulation aligns with the work of A.D. Chernin et al., where the dark energy effective mass (Mᴅᴇ) is included as a component influencing the dynamics of large-scale structures. When the apparent mass dominates, the effective mass can become negative, corresponding to the repulsive effect of dark energy.

3. The Nature of Dark Energy Before the Big Bang

Before the Big Bang, the concept of gravitational potential and dark energy as we understand them today may not have existed in the same manner. In ECM, potential energy requires the presence of mass-energy interactions, space, and time—all of which were non-existent before the Big Bang event. Thus, dark energy, in its present form, would not have existed as an independent entity.

For further insights into the conceptual foundations of existence, space, time, and energy, I recommend reviewing the following resources:

A Clear Understanding of Existence, Event, Time, and Space in Relation to Matter and Energy https://www.researchgate.net/post/A_Clear_Understanding_of_Existence_Event_Time_and_Space_in_Relation_to_Matter_and_Energy
The Nexus of Existence and Events https://www.researchgate.net/post/The_Nexus_of_Existence_and_Events
Big Bang Nucleosynthesis (Wikipedia) https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis

I appreciate your thought-provoking contributions and look forward to further discussions that challenge and refine our understanding of fundamental physics.

Best regards,

Soumendra Nath Thakur

How does a photon dynamic describe dark energy within the framework of Extended Classical Mechanics (ECM)?

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
February 10, 2025

Within Extended Classical Mechanics (ECM), photon dynamics describes dark energy by positing that photons, due to their unique properties within the framework, can exhibit a "negative apparent mass," causing them to effectively repel each other and contribute to the observed accelerating expansion of the universe, which is the primary characteristic of dark energy; this negative mass arises from the complex interaction of photon momentum and energy within the ECM equations, leading to an "effective acceleration" that counteracts gravitational pull. 

Photon Dynamics and Dark Energy in the Framework of Extended Classical Mechanics (ECM)

In the framework of Extended Classical Mechanics (ECM), photon dynamics and dark energy are intricately linked through the concepts of effective mass (Mᵉᶠᶠ) and apparent mass (Mᵃᵖᵖ). This framework provides a novel perspective on how gravitational interactions can induce mass in initially massless particles, such as photons, and how these interactions relate to the observed phenomena of dark energy.

Photon Dynamics and Effective Mass

Effective Mass and Apparent Mass:

In ECM, the effective mass (Mᵉᶠᶠ) of a photon is a dynamic property that combines the rest mass (Mᴍ​) and the apparent mass (Mᵃᵖᵖ). For photons, which have zero rest mass, their apparent mass dictates their energy-momentum exchanges and response to forces. This leads to the reformulated force equation:

Fₚₕₒₜₒₙ =−Mᵃᵖᵖ aᵉᶠᶠ

The apparent mass (Mᵃᵖᵖ) can be negative, which is crucial for understanding antigravitational effects and dark energy.

Gravitational Redshift and Photon Energy:

The total energy of a photon is analysed as the sum of its inherent energy (E) and gravitational interaction energy (Eg​). As photons escape a gravitational field, they retain their inherent energy while gradually expending their gravitational energy. This leads to gravitational redshift, where the photon's frequency shifts due to the gravitational potential.

Dark Energy and Negative Effective Mass

Dark Energy as a Gravitational Interaction:

In ECM, dark energy is not treated as a conventional field or particle but as a gravitationally interactive background that influences mass distributions at intergalactic scales. It acts on cosmic scales by modifying the gravitational potential, leading to the observed cosmic acceleration.

Negative Effective Mass and Antigravitational Effects:

The negative effective mass (Mᵉᶠᶠ<0) is a key feature of ECM, particularly in the context of dark energy. This negative mass can lead to antigravitational effects, where objects experience repulsion rather than attraction. This phenomenon echoes the behaviour of dark energy, which accelerates the universe's expansion by generating antigravitational effects.

Gravitational Mass and Dark Energy:

The gravitational mass (Mg​) in ECM is given by:

Mɢ = Mᴍ + (-Mᵃᵖᵖ)

At intergalactic scales, the interaction of dark matter with dark energy results in an effective mass contribution (Mᴅᴇ​), which is represented by:

Mɢ = Mᴍ + Mᴅᴇ

This additional inferred mass component (Mᴅᴇ) is an emergent gravitational effect, not a fundamental mass term.

Implications for Photon Dynamics and Dark Energy

Unified Framework:

ECM provides a unified framework that bridges classical mechanics, quantum principles, and cosmological implications. By incorporating the concept of apparent mass, ECM offers a cohesive mechanism to reconcile classical, quantum, and cosmological phenomena.

Cosmic Acceleration:

The negative effective mass associated with dark energy explains the observed cosmic acceleration. This antigravitational effect is crucial for understanding the expansion of the universe and the role of dark energy in shaping cosmic dynamics.

Gravitational Collapse at the Planck Scale:

At the Planck scale, gravitational interactions can induce mass in massless particles, leading to gravitational collapse. This transition from massless to massive states is a direct consequence of ECM's mass induction principle, where increasing energy (via frequency) leads to mass acquisition.

Conclusion

The framework of Extended Classical Mechanics (ECM) offers a detailed and nuanced understanding of photon dynamics and dark energy. By incorporating the concepts of effective mass and apparent mass, ECM provides a unified perspective on gravitational interactions across quantum and cosmological scales. This approach not only aligns with fundamental principles but also offers potential explanations for cosmic-scale phenomena involving dark matter, dark energy, and exotic gravitational effects.

#photondynamics #darkenergy #ECM

References:

·                     EasyChair 2024/11/28

·                     A Nuanced Perspective on Dark Energy: Extended Classical …

·                     This study presents an advanced extension of classical mechanics to examine photon dynamics and its parallels with cosmological phenomena, particularly dark energy. …

 

·                     EasyChair 2024/11/28

·                     A Nuanced Perspective on Dark Energy: Extended Classical …

·                     A Nuanced Perspective on Dark Energy: Extended Classical Mechanics Soumendra Nath Thakur November 27, 2024 Abstract This study presents an advanced …

 

·                     telitnetwork.itgo.com

·                     Photon Dynamics under Negative Apparent Mass and Effective …

·                     In the framework of Extended Classical Mechanics (ECM), "photon dynamics under negative apparent mass and effective acceleration" describes the concept that photons, when viewed …

 

·                     arXiv.org 2024/10/29

·                     [2410.22424] Early Dark Energy Effects on the 21cm Signal

·                     In this paper, we study the impact of EDE on the 21cm signal, a powerful probe of cosmic dawn, and the epoch of reionization. First, we examine the signatures of the shift in …

 

·                     EasyChair

·                     A Dual Framework for Rest and Motion States: Energy and …

·                     III. Negative Effective Mass: A central feature of the ECM framework is the concept of negative effective mass (Mᵉᶠᶠ < 0), which emerges in Case 2, when an object with zero matter mass is in …

·                     itgo.com

·                     The Massless-to-Massive Transition: Gravitational Thresholds …

·                     Conversely, ECM also explores how antigravitational interactions could reduce mass, potentially leading to negative effective mass under certain conditions. This perspective challenges …

 

·                     arXiv.org 2024/12/06

·                     Cosmological constraints on dark energy models using DESI …

·                     Hence, we have examined four popular parameterized dark energy models in our analysis: the Chevallier-Polarski-Linder (CPL), Barboza-Alcaniz (BA), Jassal-Bagla …

 

·                     ResearchGate 2024/12/22

·                     A Nuanced Perspective on Dark Energy: Extended Classical …

·                     This research introduces an advanced framework in extended classical mechanics to explore photon dynamics and its connection to cosmological phenomena, particularly dark …

 

·                     Wiley Online Library 2014/12/02

·                     Interaction between Dark Matter and Dark Energy and the …

·                     In this paper we have studied an interacting model in which the dark sectors (dark matter and dark energy) are coupled to each other in a background gravitational field which is …

 

·                     arXiv.org 2025/01/05

·                     [2501.02592] Parametrization Framework for the Deceleration …

·                     Our method provides a framework that is independent of the model to explore dark energy, leading to a deeper and more subtle understanding of the mechanisms driving late …

 

·                     Astronomy & Astrophysics (A&A)

·                     A unifying theory of dark energy and dark matter: Negative …

·                     Despite this initial intellectual hurdle, the basic properties of negative masses still make them a powerful and compelling candidate for providing a unification of dark matter and dark energy …

 

·                     EasyChair 2024/11/22

·                     Photon Dynamics in Extended Classical Mechanics: Effective …

·                     entum interactions into the extended classical mechanics framework, while also drawing parallels with the behaviour of dark energy. This approach not only enriches the …

 

·                     arXiv.org 2015/12/02

·                     [1512.00541] Massive Photon and Dark Energy - arXiv.org

·                     We investigate cosmology of massive electrodynamics and explore the possibility whether massive photon could provide an explanation of the dark energy.

 

·                     ResearchGate 2024/12/25

·                     A Dual Framework for Rest and Motion States: Energy and Mass …

·                     For the former, total energy is dominated by potential energy, with no contribution from kinetic energy. In contrast, the latter involves negative effective mass (Mᵉᶠᶠ<0) and energy...

 

·                     Oxford Academic 2022/01/29

·                     Dark matter haloes in interacting dark energy models: …

 

·                     ResearchGate 2024/11/25

·                     Equations that Bridges Extended Classical Mechanics and …

·                     From extended classical mechanics, the effective mass Mᵉᶠᶠ plays a central role in the dynamics of massless particles, including photons. It is defined as: • Mᴍ is the matter …

 

·                     Springer 2024/10/15

·                     Interacting Dark Energy and Its Implications for Unified Dark Sector

·                     The three models that are considered in this study are time-varying $$\varvec{\Lambda }$$ , Generalized Chaplygin Gas (GCG), and K-essence. Each model …

 

·                     ResearchGate 2024/12/02

·                     Matter-to-Antimatter Transition: Dynamics of Negative Apparent …

·                     As the electron's velocity increases toward the speed of light, the negative apparent mass (−Mᵃᵖᵖ) becomes dominant, reducing the effective mass (Mᵉᶠᶠ). When the velocity …

 

·                     arXiv.org 2023/01/19

·                     [2301.08743] Cosmological implications of an interacting model of …

·                     We have assumed the gravitational interaction between the matter fields i.e. between barotropic fluid and the dark energy. The dark energy evolution within the framework …

 

·                     Preprints 2024/11/29

·                     A Nuanced Perspective on Dark Energy: Extended Classical …

·                     This study presents an advanced extension of classical mechanics to examine photon dynamics and its parallels with cosmological phenomena, particularly dark energy. …

 

·                     ScienceDirect 2023/05/01

·                     Cosmological implications of an interacting model of dark matter …

·                     We have assumed the gravitational interaction between the matter fields i.e. barotropic fluid and the dark energy. The dark energy evolution is within the framework of …

 

·                     arXiv.org 2024/10/07

·                     Dark Energy, and a Dark Fluid, from topology and a massless spinor

·                     Under the existence of a massless spinor degrees of freedom in a spacetime with internal boundaries, such as black holes, we show that a topological mechanism naturally …

 

·                     repository.tudelft.nl

·                     Photon Pressure with an Effective Negative Mass Microwave Mode

·                     Here, we engineer a microwave mode in a superconducting LC circuit that mimics the dynamics of a negative mass oscillator, and couple it via photon pressure to a second low-frequency circuit.

 

·                     ScienceDirect 2023/12/01

·                     Effect of massive graviton on dark energy star structure

·                     In the following, assuming different values of free parameters defined in massive gravity, we calculate the properties of dark energy stars such as radial pressure, transverse …

 

·                     Physical Review Link Manager 2024/12/18

·                     Interacting Dark Energy after DESI Baryon Acoustic Oscillation ...

·                     We investigate the implications of the baryon acoustic oscillations measurement released by the Dark Energy Spectroscopic Instrument for interacting dark energy (IDE) …

 

·                     EasyChair

·                     Extended Classical Mechanics: Vol-1 - Equivalence Principle, …

·                     extended classical mechanics, including effective mass, dark energy, and gravitational forces, redefined to incorporate the effects of dark energy and negative mass on both local and …

 

·                     Physical Review Journals

·                     Supplemental Material for: Photon-Pressure with an Effective …

·                     With similar considerations, we find that the friction force in a stable negative-mass oscillator needs to act opposite to the usual friction force. This means it will add energy instead of …

 

·                     arXiv.org 2005/05/06

·                     [astro-ph/0505133] Effective equation of state for dark energy ...

·                     We find that the effective EOS can correspond to both normal quintessence and phantom dark energy, depending on the value of a single parameter of the RG model. We …

 

·                     ScienceDirect 2020/12/01

·                     Interacting dark energy in the early 2020s: A promising solution to …

·                     We examine interactions between dark matter and dark energy in light of the latest cosmological observations, focusing on a specific model with coupling proportional to the dark …

 

·                     Astronomy Stack Exchange 2023/09/20

·                     Is dark matter made from the particles that had charge but no …

·                     Charged, massless particles would be a form of "hot" dark matter. i.e. A form of energy density that was relativistic at the epoch of structure formation and of course, still …

 

·                     arXiv.org 2025/02/10

·                     Robustness of Dark Energy Phenomenology Across Different …

·                     While this parameterization is by far the most common, recent research has raised some questions about its utility and urged caution when interpreting it (e.g. [74, 73, 75, …

 

·                     Physical Review Journals 2024/07/22

·                     Hot new early dark energy bridging cosmic gaps: Supercooled …

·                     We propose a simple model that can alleviate the tension while remaining consistent with big bang nucleosynthesis (BBN). It is based on a dark sector described by a …

 

·                     TU Delft Research Portal

·                     Photon Pressure with an Effective Negative Mass Microwave Mode

·                     We demonstrate that the effective negative mass dynamics lead to an inversion of dynamical backaction and to sideband cooling of the low-frequency circuit by a blue-detuned pump field, …

 

·                     Nature 2020/02/19

·                     Measurement of the quantum geometric tensor and of the

·                     In this work, we present a direct measurement of the full momentum space QGT (Berry curvature and quantum metric) of the 2D bands of a homogeneous system...

 

·                     EasyChair 2025/01/06

·                     A Dual Framework for Rest and Motion States: Energy and Mass …

·                     This study explores the foundational equations of Extended Classical Mechanics (ECM), offering a comprehensive framework for analysing energy and force interactions …

 

·                     ResearchGate 2025/01/08

·                     INFLUENCE OF INTERACTIONS BETWEEN DARK ENERGY …

·                     Dark matter drives cosmic structure formation through gravitational effects, while dark energy accelerates universal expansion. Although the ΛCDM model assumes minimal …

 

·                     Physical Review Journals 2023/11/28

·                     Boson stars in massless and massive scalar-tensor gravity

·                     We study phenomenological features and stability of boson stars in massless and massive scalar-tensor theory of gravity with Damour-Esposito-Far`ese coupling.

 

·                     Physical Review Link Manager 2020/10/08

·                     Unified framework for early dark energy from α -attractors

·                     One of the most appealing approaches to ease the Hubble tension is the inclusion of an early dark energy (EDE) component that adds energy to the Universe in a narrow redshift …

 

·                     SMU Tian Lab

·                     THE EFFECTIVE MASS THEORY - SMU

·                     effective mass of the carriers is much larger or much smaller than m0. The effective mass may be anisotropic, and it may even be negative. The important point is that the electron in a periodic …

 

·                     IntechOpen 2016/11/05

·                     Superfluid Quantum Space and Evolution of the Universe

·                     In short, a photon would be a spinning phonon through superfluid dark energy, whose mechanical interaction with dark energy’s quanta would excite them, producing the …

 

·                     IntechOpen

·                     Dark Matter and Dark Energy in Galaxies Via Gravitational Field …

·                     This theory provides an explanation for the dark matter and dark energy in galaxies and the universe as due to the relativistic mass associated with gravitational and cosmological redshift …

 

·                     Springer

·                     Behavior of quasinormal modes and Van der Waals-like …

·                     Abstract In this work, we utilize the quasinormal modes (QNMs) of a massless scalar perturbation to probe the Van der Waals-like small and large black holes (SBH/LBH) phase transition of …

 

·                     IOPscience 2016/08/12

·                     Dark matter and dark energy interactions: theoretical challenges ...

·                     Models where dark matter and dark energy interact with each other have been proposed to solve the coincidence problem. We review the motivations underlying the need to …

 

·                     Preprints 2024/11/25

·                     Photon Dynamics in Extended Classical Mechanics: Effective …

·                     In essence, this research aims to refine our understanding of photon dynamics by integrating concepts of effective mass, negative inertia, and energy-momentum interactions …

 

·                     arXiv.org 2022/12/14

·                     Photon-Pressure with an Effective Negative Mass Microwave Mode

·                     We demonstrate that the effective negative mass dynamics lead to an inversion of dynamical backaction and to sideband-cooling of the low-frequency circuit by a blue-detuned …

 

·                     SciTechDaily 2024/12/08

·                     Rewriting Cosmic History: DESI’s New Map Challenges …

·                     Research using DESI data reveals dark energy’s dynamic nature, supporting the quintom-B model and suggesting a non-static cosmological constant.

 

·                     EasyChair 2024/11/22

·                     Photon Dynamics in Extended Classical Mechanics: Effective …

·                     This research explores the concept of photon dynamics, specifically focusing on the notion of effective mass (Mᵉᶠᶠ) and its implications for force interactions and energy …

 

·                     ScienceDirect 2020/12/01

·                     Can massive neutrinos be responsible for late time phase …

·                     In our opinion, the turning of massive neutrinos from relativistic to non-relativistic might cause a phase transition at late times. We implement this idea using massless λ ϕ 4 …

 

·                     American Institute of Mathematical Sciences 2016/11/02

·                     Gravitational Field Equations and Theory of Dark Matter and Dark …

·                     Both particles can be considered as gravitational force carriers, and as they are massless, the induced forces are long-range forces. The (nonlinear) interaction between these bosonic …

 

·                     Nature 2025/02/05

·                     Quantum coarsening and collective dynamics on a programmable …

·                     The total classical energy of the system is conserved whereas the bulk (domain wall) energy increases (decreases). Inset: the separation of domains into bulk and domain walls for …

 

·                     arXiv.org 2023/02/23

·                     [2302.11949] Interacting dark energy: clarifying the cosmological ...

·                     In this study, cosmological models are considered, where dark matter and dark energy are coupled and may exchange energy through non-gravitational interactions with one …

 

·                     arXiv.org 2023/09/16

·                     [2401.13814] Illuminating the Dark Sector: Searching for new ...

·                     In this dissertation, we delve into extensions to the standard model that consider alternatives to the mysterious nature of the dark sector and any possible new interactions …

 

·                     Oxford Academic 2024/09/13

·                     Early galaxies and early dark energy: a unified solution to the …

·                     JWST has revealed a large population of UV-bright galaxies at |$z\gtrsim 10$| and possibly overly massive galaxies at |$z\gtrsim 7$|⁠, challenging standard galaxy formation …

 

·                     Papers With Code 2020/09/30

·                     Unified framework for Early Dark Energy from $\alpha$-attractors

·                     One of the most appealing approaches to ease the Hubble tension is the inclusion of an early dark energy (EDE) component that adds energy to the Universe in a narrow …

 

·                     iaspoint.com 2025/01/10

·                     Dark Energy and the Timescape Model in Cosmology

·                     Dark energy constitutes about 70% of the universe’s total energy, influencing cosmic expansion. It is essential in the Lambda-CDM model, which is the prevailing …

 

·                     Physical Review Link Manager 2024/05/17

·                     Photon Pressure with an Effective Negative Mass Microwave Mode

·                     We demonstrate that the effective negative mass dynamics lead to an inversion of dynamical backaction and to sideband cooling of the low-frequency circuit by a blue-detuned …