Consistency in Interpreting Empirical and Abstract Evidence: Avoiding Hasty Judgments.

Soumendra Nath Thakur 

February 12, 2025

The phrase "absence of evidence is not evidence of absence" conveys that a lack of evidence does not necessarily mean something does not exist. This statement is generally valid, as it warns against assuming nonexistence solely due to missing evidence.

However, the phrase "is not evidence of absence" oversimplifies the issue. While absence of evidence does not always confirm nonexistence, it can sometimes serve as evidence of absence, depending on the context. The statement challenges flawed reasoning that always equates absence of evidence with nonexistence. However, it does not fully acknowledge that, under certain conditions, absence of evidence can contribute to an argument for nonexistence. Ideally, the statement should emphasize the possibility of presence rather than implying a definite presence or absence.

This phrase functions as a rhetorical counter to hasty judgments. If someone assumes that missing evidence automatically means nonexistence, the phrase offers a clever rebuttal. However, its strength lies in questioning premature conclusions rather than establishing a definitive logical rule.

In mathematics, especially in abstract reasoning, not all conclusions require empirical evidence. Dismissing mathematical constructs simply because they lack direct evidence would be inconsistent, as abstract mathematics is grounded in logical principles rather than empirical validation. While these principles can apply to real-world phenomena, their validity does not depend on physical evidence alone.

The Formulation and Implications of Extended Classical Mechanics (ECM)

RG Discussion Link

Soumendra Nath Thakur, ORCiD: 0000-0003-1871-7803, 

Tagore’s Electronic Lab, India. 

Communication: postmasterenator@gmail.com

 

February 12, 2025

 

Abstract

 

Extended Classical Mechanics (ECM) introduces a modified formulation of classical mechanics by redefining mass as effective mass (Mᵉᶠᶠ), which incorporates both matter mass (Mᴍ) and apparent mass (Mᵃᵖᵖ). This approach allows for a broader interpretation of gravitational interactions, particularly in systems where negative effective mass induces repulsive effects. ECM extends Newtonian dynamics by establishing force and energy equations for both massive and massless entities, naturally integrating with quantum mechanical principles. The framework provides a novel explanation for cosmic expansion, where massless particles experience repulsive gravitational effects due to their apparent mass contributions. Additionally, ECM introduces conditions for superluminal motion and refines the concept of the Hubble radius, offering insights into observational horizons and large-scale structure formation. The implications of ECM suggest a fundamental link between gravity, mass-energy equivalence, and large-scale cosmic evolution.

 

Keywords: apparent mass (Mᵃᵖᵖ), effective mass (Mᵉᶠᶠ), gravitational interactions, cosmic expansion, superluminal motion, Hubble radius, [Apparent Weight] [Dark Energy] [ECM] [Extended Photon Dynamics] [Gravitational Collapse] [Massless-to-Massive] [Photon Phases] [Inertial mass relativistic gravity] [Extended Classical Mechanics] [About]

 

1. Classical Mechanics Framework

 

In traditional mechanics, force is defined as the product of mass and acceleration. The total energy of a system consists of potential and kinetic energy, where potential energy follows an inverse proportionality with distance in gravitational systems, while kinetic energy depends on the squared velocity of the moving object.

 

F = ma

Eₜₒₜₐₗ = PE + KE = −GMm/r + 1/2mv²

 

#Mathematical denotation terms are listed alphabetically under 'Mathematical terms used,' with brief descriptions below and apply to all equations in this study.

 

2. ECM Force for Matter Mass

 

ECM modifies Newton’s second law by redefining mass as effective mass Mᵉᶠᶠ. Within the Extended Classical Mechanics framework, force is derived by incorporating both matter mass and apparent mass. The resultant force is expressed in terms of effective mass and acceleration, allowing for a broader interpretation of gravitational interactions, particularly in systems where negative effective mass induces repulsive effects.

 

Fᴇᴄᴍ = (Mᴍ −Mᵃᵖᵖ)aᵉᶠᶠ

Fᴇᴄᴍ = Mᵉᶠᶠaᵉᶠᶠ, since, (Mᴍ −Mᵃᵖᵖ) = Mᵉᶠᶠ, Mᴍ = 0, Mᵉᶠᶠ < 0.

 

This suggests that when effective mass is negative, the force direction may lead to repulsive gravitational effects, impacting large-scale cosmic structures.

 

3. ECM Force for Massless Particles

 

For massless entities such as photons, force is governed by apparent mass contributions, as there is no direct matter mass component. In ECM, this negative effective mass leads to repulsive gravitational interactions, offering a natural explanation for certain cosmic expansion effects.

 

Since the force depends solely on the apparent mass, the equation takes an alternative form when effective mass is negative, reinforcing its connection to observed large-scale repulsive behavior in the universe.

 

Fₚₕₒₜₒₙ = −Mᵃᵖᵖaᵉᶠᶠ , since Mᴍ = 0

Fₚₕₒₜₒₙ = Mᵉᶠᶠaᵉᶠᶠ ,  since (Mᴍ −Mᵃᵖᵖ) = Mᵉᶠᶠ, Mᴍ = 0, Mᵉᶠᶠ < 0.

 

This formulation suggests that, under negative effective mass conditions, repulsive gravitational effects emerge naturally, influencing cosmic expansion and the large-scale distribution of matter.

 

4. ECM Energy-Frequency Relationship for Massless Systems

 

The energy-frequency relation in ECM aligns with the established principles of quantum mechanics, where the effective mass of a massless particle is proportional to its frequency. This correspondence reinforces the compatibility of ECM with existing quantum formulations.

 

Mᵉᶠᶠ,ₘₐₛₛₗₑₛₛ = hf/c² = E/c²

 

5. ECM Kinetic Energy of Apparent Mass

 

The kinetic energy of a system influenced by apparent mass follows a modified classical approach. Instead of a strictly positive mass contribution, apparent mass is taken into account with its sign reversed, modifying the total kinetic energy expression. This approach provides a framework for analyzing phenomena where negative mass effects play a significant role.

 

KEₚₕₒₜₒₙ = 1/2(−Mᵃᵖᵖ)·c².

 

Here, apparent mass Mᵃᵖᵖ is considered in the kinetic energy equation.

 

6. ECM Energy for Matter Mass Systems

 

Total energy in ECM consists of potential and kinetic components, with potential energy derived from the effective mass terms. The interaction of matter mass and apparent mass defines the energy distribution, ensuring consistency with classical interpretations while extending the framework to incorporate novel effects. Under the influence of ECM force, kinetic energy contributions arise from apparent mass components.

 

Eₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ

Mᴍ ⇒ PEᴇᴄᴍ, −Mᵃᵖᵖ ⇒ KEᴇᴄᴍ, when ECM force is active                                               

 

7. ECM Energy Formulation for Massless and Effective Mass Systems

 

In ECM, the total energy of a system—including massless entities—retains contributions from both potential energy (PE) and kinetic energy (KE). The potential energy follows an effective mass formulation, while kinetic energy depends on relative velocity conditions.

 

• When effective mass is positive, motion remains subluminal (v ≤ c).

• When effective mass is negative, velocities exceeding c become possible. However, in this case, the superluminal velocity should be interpreted as an emergent property of the effective energy framework, rather than a direct physical motion of particles exceeding c.

 

Total Energy Equations:

 

Eₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ = {−G(Mᴍ −Mᵃᵖᵖ)(mₘ−mᵃᵖᵖ)/r )} + 1/2(mₘ−mᵃᵖᵖ)v²;

v ≤ c when Mᴍ ≥−Mᵃᵖᵖ, but v ≥ c when Mᴍ ≤ −Mᵃᵖᵖ .

 

Eₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ = (−GMᵉᶠᶠmᵉᶠᶠ/r ) + 1/2mᵉᶠᶠv²

v ≤ c when Mᵉᶠᶠ > 0, but v ≥ c when Mᵉᶠᶠ < 0

 

Eₘₐₛₛₗₑₛₛ = 1/2(−mᵃᵖᵖ)v²; v = c.

 

8. Dual Representation of Effective Mass

 

ECM introduces a dual representation of effective mass, distinguishing between larger system mass contributions and localized test particle effects. This distinction is analogous to classical gravitational potential energy equations, where mass terms represent both global and local contributions.

 

Mᵉᶠᶠ,ₘₐₛₛₗₑₛₛ = hf/c² = E/c²

mᵉᶠᶠ,ₘₐₛₛₗₑₛₛ = hf/c² = E/c²

 

The notations serve a similar dual-mass representation:

Mᵉᶠᶠ refers to the effective mass of the larger system (analogous to M in gravitational potential energy).

 

9. Kinetic Energy Representation of Apparent Mass in ECM - Massless Case):

 

In the ECM framework, the kinetic energy of an apparent mass in a massless system adheres to the energy-frequency relation. The apparent mass is expressed in terms of energy and frequency, maintaining consistency with quantum mechanics. This formulation aligns with the mass-energy equivalence principle, reinforcing the role of induced mass-like effects in ECM.

 

The equation:

 

−Mᵃᵖᵖ,ₘₐₛₛₗₑₛₛ = hf/c² = E/c²

 

This describes the apparent mass associated with massless entities like photons, and follows from the mass-energy equivalence principle.

 

10. Total Effective Mass with Gravitational Contributions

 

The total effective mass in ECM includes contributions from gravitational energy. This formulation incorporates frequency-dependent terms, where Δf represents a gravitationally induced frequency shift due to energy contributions from gravitational fields. The presence of this additional frequency shift component extends the effective mass concept beyond conventional mass-energy equivalence principles.

 

Mᵉᶠᶠ,ₜₒₜₐₗ = Mᵉᶠᶠ,ₘₐₛₛₗₑₛₛ + Eg/c² = hf/c² + hΔf/c²

 

This equation represents the total effective mass in ECM, which includes contributions from:

 

• The mass-energy equivalence of a massless particle (e.g., a photon) with frequency f.

• An additional gravitational energy term associated with the frequency shift Δf, which arises due to gravitational interactions.

 

11. Implications of Superluminal Velocities & Hubble Radius in ECM  

 

In Extended Classical Mechanics (ECM), negative effective mass can induce anti-gravitational effects at extreme cosmic distances. This contributes to accelerated cosmic expansion and influences large-scale structure dynamics. The observational limit beyond the Hubble radius arises due to recession velocities surpassing the speed of light, preventing information retrieval from beyond this boundary.

 

For v = c = 3 × 10⁸ m/s, the Hubble radius is given by:

 

d = v/H₀ = (3 × 10⁸ m s⁻¹) / (2.268 × 10⁻¹⁸ s⁻¹) = 1.32 × 10²⁶ m

 

Converting to light-years:

 

d = 1.32 × 10²⁶ m × (1 light-year/9.461 × 10¹⁵ m) = 13.93 billion light-years

 

At this proper distance, known as the Hubble radius, the recession velocity reaches the speed of light. Beyond this threshold, galaxies move at superluminal speeds, making them observationally inaccessible.

 

This ECM interpretation provides a structured perspective on observational horizons, emphasizing the role of effective mass variations in shaping cosmic expansion and defining observational limits imposed by superluminal recession.

 

12. Variation of Apparent Mass Across Local and Intergalactic Scales in ECM

 

In Extended Classical Mechanics (ECM), apparent mass (Mᵃᵖᵖ) plays a critical role in determining the effective mass (Mᵉᶠᶠ) and, consequently, gravitational interactions. The influence of apparent mass varies significantly across different cosmic scales:

 

Local, Planetary, and Stellar Scales: The high density of ordinary matter results in dominant gravitational effects, leading to minimal changes in apparent mass. Dark matter’s contribution to gravitational interactions is negligible at these scales.

 

Galactic Scale: Dark matter dominates mass distribution, comprising ~85% of a galaxy’s total mass. As a result, its gravitational influence exceeds that of normal matter, leading to a stronger reduction in apparent mass and an overall increase in the strength of gravitating mass (Mɢ).

 

Intergalactic Scale: The effect of dark matter on apparent mass becomes even more pronounced, with its gravitational influence intensifying over vast cosmic distances. This drives large-scale structure formation and influences the expansion dynamics of galaxy clusters.

 

These variations in apparent mass across scales highlight how gravitational interactions are governed by effective mass (Mᵉᶠᶠ) = Mᴍ − Mᵃᵖᵖ, where an increase in gravitational strength results in a corresponding increase in negative apparent mass, further lowering effective mass.

 

Reference Papers:

 

1.                  Chernin, A. D., Бисноватый-коган, Г. С., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013a). 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., Understanding Photon Interactions: Source Gravitational Wells vs. External Fields. (2024). ResearchGate. https://doi.org/10.13140/RG.2.2.14433.48487

 

3.                  Thakur, S. N., & Bhattacharjee, D. (2023b). Phase shift and infinitesimal wave energy loss equations. Journal of Physical Chemistry & Biophysics, 13(6), JPCB-23-27248 (R). https://www.longdom.org/open-access/phase-shift-and-infinitesimal-wave-energy-loss-equations-104719.html

 

4.                  Thakur, S. N. (2023). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature. Definitions. https://doi.org/10.32388/81iiae

 

5.                  Thakur, S. N. (2023). The dynamics of photon momentum exchange and curvature in gravitational fields. Definitions. https://doi.org/10.32388/r625zn

 

6.                  Thakur, S. N. (2023). Redshift and its Equations in Electromagnetic Waves. ResearchGate. https://doi.org/10.13140/RG.2.2.33004.54403

 

7.                  Thakur, S. N. (2023). Cosmic Speed beyond Light: Gravitational and Cosmic Redshift. ResearchGate. https://doi.org/10.13140/RG.2.2.36400.94721

 

8.                  Thakur, S. N., Bhattacharjee, D., & Frederick, O. (2023). Photon Interactions in Gravity and Antigravity: Conservation, Dark Energy, and Redshift Effects. Preprints.org. https://doi.org/10.20944/preprints202309.2086.v1

 

*-*-*-*-*

About the Formulation and Implications of Extended Classical Mechanics (ECM)

 

Soumendra Nath Thakur's work on Extended Classical Mechanics (ECM) offers a comprehensive and nuanced exploration of how classical mechanics can be extended to encompass phenomena typically associated with quantum mechanics and cosmology. Here’s a brief comment on the key points and implications of ECM:

 

1. Classical Mechanics Framework

Thakur begins by grounding ECM in traditional mechanics, where force is defined as the product of mass and acceleration, and total energy consists of potential and kinetic components. This foundational understanding is crucial for extending classical mechanics to more complex systems.

2. ECM Force for Matter Mass

ECM modifies Newton’s second law by introducing the concept of effective mass (Mᵉᶠᶠ), which combines matter mass (Mᴍ) and apparent mass (Mᵃᵖᵖ). This modification allows for a broader interpretation of gravitational interactions, particularly in systems where negative effective mass induces repulsive effects. This is a significant departure from traditional mechanics and opens up new avenues for understanding gravitational dynamics.

3. ECM Force for Massless Particles

For massless entities like photons, ECM posits that force is governed by apparent mass contributions. This leads to repulsive gravitational interactions, offering a natural explanation for cosmic expansion effects. This formulation suggests that negative effective mass conditions can lead to repulsive gravitational effects, influencing cosmic expansion and the large-scale distribution of matter.

4. ECM Energy-Frequency Relationship for Massless Systems

The energy-frequency relation in ECM aligns with quantum mechanics, where the effective mass of a massless particle is proportional to its frequency. This correspondence reinforces the compatibility of ECM with existing quantum formulations, bridging classical and quantum mechanics.

5. ECM Kinetic Energy of Apparent Mass

The kinetic energy of a system influenced by apparent mass follows a modified classical approach. This approach accounts for negative mass effects, modifying the total kinetic energy expression. This framework is essential for analyzing phenomena where negative mass effects play a significant role.

6. ECM Energy for Matter Mass Systems

Total energy in ECM consists of potential and kinetic components, with potential energy derived from effective mass terms. The interaction of matter mass and apparent mass defines the energy distribution, ensuring consistency with classical interpretations while extending the framework to incorporate novel effects.

7. ECM Energy Formulation for Massless and Effective Mass Systems

ECM introduces a dual representation of effective mass, distinguishing between larger system mass contributions and localized test particle effects. This distinction is crucial for understanding how gravitational interactions are governed by effective mass across different scales.

8. Implications of Superluminal Velocities & Hubble Radius in ECM

ECM suggests that negative effective mass can induce anti-gravitational effects at extreme cosmic distances, contributing to accelerated cosmic expansion. This interpretation provides a structured perspective on observational horizons, emphasizing the role of effective mass variations in shaping cosmic expansion and defining observational limits imposed by superluminal recession.

9. Variation of Apparent Mass Across Local and Intergalactic Scales in ECM

ECM highlights how the influence of apparent mass varies significantly across different cosmic scales. At local, planetary, and stellar scales, gravitational effects are dominated by ordinary matter. At galactic and intergalactic scales, dark matter's gravitational influence becomes more pronounced, driving large-scale structure formation and influencing the expansion dynamics of galaxy clusters.

Conclusion

Soumendra Nath Thakur's work on ECM offers a detailed and nuanced understanding of gravitational interactions across quantum and cosmological scales. By introducing the concepts of effective mass and apparent mass, ECM provides a unified framework that bridges classical mechanics, quantum principles, and cosmological phenomena. 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. Thakur's work encourages further exploration and refinement of ECM in various physical

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 …