Mass Concepts in Classical, Relativistic, and Extended Classical Mechanics (ECM):

February 19, 2025

The book Concepts of Mass in Classical and Modern Physics by Max Jammer presents traditional mass concepts, primarily defining mass as either inertial mass or rest mass. However, these descriptions do not account for dynamic effective mass or apparent mass.

Extended Classical Mechanics (ECM) expands upon these conventional definitions by introducing negative apparent mass and negative effective mass, extending the concept of mass beyond ordinary matter to include the effects of dark matter. This distinction is crucial in understanding mass interactions at different cosmic scales.

Mass Equivalence in Different Frameworks

In classical mechanics, inertial mass is equivalent to gravitational mass: 

m = m𝑔 

​In relativistic mechanics, rest mass (invariant mass) is also equated to gravitational mass: 

m = m𝑔

​In Extended Classical Mechanics (ECM), gravitating mass (Mɢ) is equivalent to effective mass (Mᵉᶠᶠ), which includes both matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ):

Mɢ = Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

where matter mass (Mᴍ) is the combined mass of ordinary matter (Mᴏʀᴅ) and dark matter mass (Mᴅᴍ):

Mᴍ = Mᴏʀᴅ + Mᴅᴍ 

Effective Mass at Celestial and Galactic Scales

At celestial or planetary scales within a galaxy, effective mass (Mᵉᶠᶠ) can be either positive or negative, depending on the balance between matter mass and negative apparent mass:

If matter mass dominates (Mᴍ > Mᵃᵖᵖ), then effective mass is positive:

Mᵉᶠᶠ > 0

If negative apparent mass dominates (Mᵃᵖᵖ > Mᴍ ), then effective mass becomes negative:

Mᵉᶠᶠ < 0

The ECM expression for gravitating mass can also be rewritten as:

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

This formulation aligns conceptually with the expression discussed by A. D. Chernin et al. in Dark Energy and the Structure of the Coma Cluster of Galaxies:

Mɢ = Mᴍ + Mᴅᴇ, 

where Mᴅᴇ represents the effective mass of dark energy, which is always negative:

Mᴅᴇ < 0

While ECM extends this concept by incorporating negative apparent mass alongside dark energy effects, both frameworks recognize the role of negative mass contributions in gravitational dynamics.

This framework provides a more comprehensive approach to understanding mass interactions in the universe, bridging the gap between classical mechanics and modern astrophysical observations.

Author:

Soumendra Nath Thakur

Summary: Photon Energy Conservation and Gravitational Lensing in Extended Classical Mechanics:

February 18, 2025

Extended Classical Mechanics (ECM) establishes a conservation framework for photon energy interactions within the curvature of gravitational fields. By extending the energy-momentum relation p = hf/c to include apparent mass (Mᵃᵖᵖ) and negative inertia, ECM reveals that gravitational lensing involves a symmetric energy exchange. As a photon follows the curvature of a gravitational field, it undergoes a blueshift when approaching a gravitational well, gaining energy, and a redshift when receding, losing energy. This process maintains the photon's intrinsic energy (E) while offering a clear explanation for both light bending and its energy transformation in gravitational fields.

#ECMinterpretation #GravitationalLensing in #gravitationalfield not in #curvatureinspacetime #GravitationalLensingInECM

About Black Hole Motion, Negative Apparent Mass, and Galactic Recession in Extended Classical Mechanics (ECM):

Author: Soumendra Nath Thakur  

Date: February 18, 2025

Introduction

Extended Classical Mechanics (ECM) challenges the conventional view of black holes as stationary entities. Instead, they are dynamic, with motion exceeding the speed of light, dictated by the ratio of wavelength to time period surpassing the Planck scale limit.

Key Concepts

1. Black Holes and Motion:

   - Originating from gravitational collapse, black holes must exhibit rapid motion.

   - This motion is a result of their unique properties, going beyond the speed of light.

2. Transformation During Gravitational Collapse:

   - The baryonic mass of a massive body undergoes a transformation into negative apparent mass (-Mᵃᵖᵖ) during collapse.

   - This leads to a corresponding negative effective mass (Mᵉᶠᶠ < 0), altering the object's behavior.

3. Anti-Gravitational Properties:

   - The negative apparent mass gives black holes anti-gravitational properties.

   - This causes them to move away from gravitational wells, actively accelerating.

4. Galactic Interaction:

   - The interaction between a black hole's negative effective mass and the galaxy's positive effective mass creates a binding effect.

   - This keeps the black hole within the galaxy, rather than allowing it to escape.

5. Galactic Recession:

   - The entire galaxy undergoes recession, influenced by the interplay of effective masses.

   - This provides an alternative explanation to the large-scale recession of galaxies.

6. Local Scale Interactions:

   - Interactions between a black hole and nearby massive bodies are governed by their effective masses and force balance.

   - A black hole with a larger negative effective mass can attract nearby objects.

Conclusion

This refined interpretation offers deeper insights into black hole behavior and its impact on galactic recession and structure formation. Black holes are not just gravitational sinks but active drivers of cosmic motion, contributing to the universe's expansion. This framework provides a new perspective on the fundamental nature of black holes and their role in the universe.

About Massless Objects, Negative Effective Mass, and Anti-Gravitational Motion in Extended Classical Mechanics:

Comment:

This comment is on Extended Classical Mechanics (ECM) and massless objects! It proposes some really interesting ideas about anti-gravitational forces and energy exchange mechanisms for massless particles, going beyond conventional understandings of inertia and speed limits. The connection to Planck scales is particularly intriguing. It suggests a need for a revised understanding of how gravity interacts with objects at the quantum level.

Author: Soumendra Nath Thakur  

Date: February 18, 2925

Abstract:

This paper explores the behaviour of massless objects within the framework of Extended Classical Mechanics (ECM), proposing that these objects exhibit anti-gravitational forces due to their negative effective mass.

Key Concepts:

1. Massless Objects and Anti-Gravitational Force:

   - Massless objects possess an inherent anti-gravitational force against surrounding gravitational influences.

   - This phenomenon is attributed to their negative apparent mass (-Mᵃᵖᵖ) and negative effective mass (Mᵉᶠᶠ < 0).

2. Energy Expenditure and Interaction:

   - While interacting with gravitational fields, massless objects expend energy, which is not derived from their inherent energy.

   - They gain energy through gravitational interactions with massive bodies, retaining this energy upon escaping gravitational fields.

3. Motion Dynamics:

   - The motion of massless objects is influenced by their negative apparent mass, leading to continuous motion rather than inertia.

   - The speed of these objects is constrained by Planck scales, specifically the ratio of Planck length to Planck time.

4. Wavelength and Speed Limit:

   - If the wavelength of a massless object exceeds the minimum Planck length, its speed may surpass conventional limits, resulting in strong anti-gravitational forces.

   - This introduces a new perspective on the speed limits of massless bodies.

5. Gravitational Interactions at Quantum Scales:

   - At scales smaller than the Planck length, gravitational interactions and energy transformations behave differently, becoming imperceptible under traditional observation methods.

   - The principle of energy conservation implies that energy does not vanish but transforms into higher, undetectable energy states.

Conclusion:

The ECM framework challenges conventional mechanics by providing new insights into the motion, gravity, and energy transformation of massless objects. It opens avenues for further research into the fundamental nature of gravity and motion beyond the Planck scale.

Reference:

About Massless Objects, Negative Effective Mass, and Anti-Gravitational Motion in Extended Classical Mechanics:

Black Hole Motion, Negative Apparent Mass, and Galactic Recession in Extended Classical Mechanics (ECM):

Soumendra Nath Thakur 

February 18, 2025

According to the principles of Extended Classical Mechanics (ECM), black holes cannot be truly stationary, even though they originate from the gravitational collapse of massive bodies with rest mass and rest energy. Instead, they must exhibit motion exceeding the speed of light, as their ratio of wavelength to time period surpasses the Planck scale limit.

During gravitational collapse, the baryonic mass of a sufficiently massive body transforms into negative apparent mass (-Mᵃᵖᵖ), leading to a corresponding negative effective mass (Mᵉᶠᶠ < 0). As a result, these collapsed objects no longer exhibit the properties of conventional massive bodies. This transformation occurs when the rest mass and its associated energy convert into an energetic form, causing the baryonic mass to take on negative apparent mass properties, fundamentally altering its interaction with gravitational fields.

The intrinsic anti-gravitational nature of negative apparent mass plays a crucial role in this transformation. As a massive object undergoes gravitational collapse, it achieves immense anti-gravitational properties in accordance with ECM principles. Consequently, its effective mass (Mᵉᶠᶠ < 0) causes it to move counter to the gravitational potential of the universe. This motion is not just an inertial effect but an active acceleration away from gravitational wells, reinforcing an anti-gravitational influence on the galaxy it resides in.

However, the interaction between the negative effective mass of a black hole (Mᵉᶠᶠ < 0) and the total effective mass of the galaxy (which remains positive) results in a net binding effect. The magnitude of the galaxy’s effective mass outweighs the negative effective mass of the black hole, keeping the black hole gravitationally bound within the galaxy. As a result, rather than individual black holes escaping, the entire galaxy itself undergoes recession, accelerating away from the gravitational potential of the universe. This provides an extended interpretation of galactic motion, suggesting that the large-scale recession of galaxies is influenced by the interplay of effective masses rather than solely by dark energy.

On a local scale, the interaction between a black hole and a nearby massive body is governed by their respective effective masses and the balance between their anti-gravitational and gravitational interaction points. If the absolute magnitude of the black hole’s negative effective mass exceeds the effective mass of the nearby object (|Mᵉᶠᶠ₍BH₎| > |Mᵉᶠᶠ₍object₎|), the black hole will exert an attractive force on the nearby body, leading to accretion. This perspective refines the understanding of how black holes interact with their surroundings, both at the galactic and universal scales.

This refined interpretation not only provides a deeper insight into black hole behavior but also suggests that galactic recession and structure formation are directly influenced by the transformation of massive bodies into entities with negative effective mass. In this framework, black holes are not merely gravitational sinks but active drivers of cosmic motion, contributing to the large-scale expansion of the universe while remaining dynamically integrated within their host galaxies.