Electron’s Matter-to-Antimatter Transition: A Framework of Extended Classical Mechanics.

Soumendra Nath Thakur

December 02, 2024

Abstract:

This study explores the dynamics of an electron transitioning from matter to antimatter-like behaviour within the framework of extended classical mechanics. As the electron accelerates toward the speed of light, its matter mass (Mᴍ) diminishes, and negative apparent mass (− Mᵃᵖᵖ) becomes dominant, leading to a shift from gravitational attraction to antigravitational effects. The resulting structural implications suggest a breakdown of the electron's traditional matter form, transitioning it into a state governed by negative effective mass. These findings provide critical insights into the interplay of matter mass, apparent mass, and the forces acting in extreme conditions.

Keywords: Negative Apparent Mass, Matter Mass Transition, Antigravity Effects, Effective Mass Dynamics, Electron Structural Breakdown,

Dynamics of Negative Apparent Mass and the Matter-to-Antimatter Transition

In the context of extended classical mechanics, an important aspect of negative apparent mass (−Mᵃᵖᵖ) and how it interacts with positive matter mass (Mᴍ) as the electron accelerates, particularly when approaching high velocities. To reflect this, we need to focus on the dynamics between the electron’s matter mass and apparent mass, and how these interplay as the electron approaches the speed of light, eventually making the matter mass negligible and the apparent mass dominant. This leads to the effective mass transitioning toward negative values, which could imply a shift from gravitational attraction to antigravitational effects.

Structural Implications of Negative Apparent Mass:

As the negative apparent mass −Mᵃᵖᵖ becomes dominant, it exerts an increasing pressure on the positive matter mass of the electron, which can cause the structural integrity of the electron to be compromised.

The pressure exerted by the negative apparent mass could overwhelm the electron's normal structure, potentially leading to its disintegration or transformation into a state where the traditional concept of "matter" no longer applies in the usual sense.

The key insight here is that as the electron accelerates to high speeds, its matter mass Mᴍ becomes negligible, and the negative apparent mass −Mᵃᵖᵖ becomes dominant.

This transition leads to the effective mass becoming negative, which shifts the electron’s behaviour from gravitational attraction to antigravity.

As the kinetic energy increases, it is no longer just a result of the matter mass, but instead is primarily driven by the negative apparent mass, which could result in the electron reaching speeds near c and transitioning to a state where its structural integrity is challenged by the forces acting on it.

Electron Transition from Matter to Antimatter:

Transition from Matter to Antimatter:

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 approaches c, the matter mass (Mᴍ) effectively becomes negligible compared to the negative apparent mass. In this state, the electron could experience antigravitational effects as a result of its negative effective mass.

This leads to the electron being subjected to forces that no longer attract it to gravitational sources, but instead, these forces would push it away from those sources. This is an antigravity effect.

Structural Integrity and Breakdown:

The most critical point is that, as the negative apparent mass grows, it exerts a counteracting pressure on the structure of the electron.

This pressure is not simply a force acting against gravitational attraction; it is a fundamental change in the dynamics of the electron's existence, transitioning it from matter to something that could potentially behave like antimatter under the extreme conditions.

Gravitational Bound Systems:

In any gravitationally bound system (such as a galaxy), as an object’s speed increases and it approaches c, it becomes increasingly difficult for the object to maintain its matter mass structure.

At the limiting point, when negative apparent mass dominates, the matter mass of the electron would no longer be able to counteract the pressure from the negative apparent mass, leading to the breakdown of its structural integrity.

Thus, the electron would no longer behave as conventional matter; its behaviour would be governed by its negative effective mass, and its structure could potentially collapse or dissipate under these extreme conditions. This breakdown explains why no matter can survive as matter within a gravitationally bound system at light's speeds, where negative apparent mass takes over and results in antigravity.

In essence, the application of force to accelerate matter to light's speeds in a gravitationally bound system results in a transition from a gravitationally attractive state to a repulsive, antigravitational state governed by negative effective mass.

Conclusion:

The framework of extended classical mechanics provides a novel lens to understand the transition of an electron from matter-like behaviour to an antimatter-like state. As the electron accelerates toward the speed of light, its positive matter mass (Mᴍ) diminishes, and the negative apparent mass (−Mᵃᵖᵖ) becomes dominant. This transition redefines its effective mass (Mᵉᶠᶠ), leading to a shift from gravitational attraction to antigravitational effects. The interplay of these mass components, under extreme conditions, challenges the structural integrity of the electron, potentially transforming it beyond the traditional concept of matter. These findings elucidate a critical mechanism by which matter, under intense forces and velocities, could evolve into a state exhibiting antimatter-like properties, driven by the dominance of negative effective mass.

Description of Mathematical Terms:

1. c (speed of light): A fundamental constant in physics, representing the maximum speed within a gravitationally bound system at which information or matter can travel in a vacuum, approximately 3 × 10⁸ m/s.

2. F (force): A vector quantity representing the interaction that changes the motion of an object, calculated in extended classical mechanics as  F = (Mᴍ − Mᵃᵖᵖ)⋅aᵉᶠᶠ.

3. KE (kinetic energy): The energy an object possesses due to its motion, driven by both matter mass (Mᴍ) and negative apparent mass (− Mᵃᵖᵖ) in this context.

4. Mᵃᵖᵖ (apparent mass): A concept in extended classical mechanics representing the negative contribution to effective mass, arising from kinetic energy or other dynamic effects.

5. Mᵉᶠᶠ (effective mass): The net mass of a system combining matter mass (Mᴍ) and apparent mass (Mᵃᵖᵖ), expressed as Mᵉᶠᶠ = Mᴍ − Mᵃᵖᵖ. It governs the dynamic response to forces.

6. Mᴍ (matter mass): The intrinsic positive mass of an object, such as an electron, representing its rest mass without motion effects.

7. Mᴍ,ᴘᴇ (matter mass potential energy): The contribution to energy arising from the object's position within a potential field, linked to its intrinsic mass (Mᴍ).

8. Mᵃᵖᵖ,ᴋᴇ (apparent mass kinetic energy):The kinetic energy associated with the negative apparent mass, highlighting the dominant role of Mᵃᵖᵖ at high velocities.

9. PE (potential energy): Energy stored in an object due to its position within a gravitational or other force field, related to Mᴍ.

10. v (velocity): The speed and direction of motion of an object. In this context, v approaches c, leading to significant effects on Mᴍ, Mᵉᶠᶠ, and F.

These terms collectively describe the dynamics of matter, apparent mass, and energy transitions in the framework of extended classical mechanics.

A Novel Interpretation in Extended Classical Mechanics:

This ground breaking paper introduces a transformative perspective on the behaviour of matter at extreme velocities, redefining classical mechanics by incorporating the concept of negative apparent mass. This novel mathematical framework has the potential to revolutionize our understanding of mass, energy, and gravitational dynamics.

Key Contributions:

• Reinterpretation of Classical Mechanics: By integrating negative apparent mass, the paper redefines classical mechanics, offering new insights into the behaviour of matter at relativistic speeds.

• Addressing Long-Standing Questions: The framework provides a fresh approach to understanding phenomena such as matter's interaction in strong gravitational fields and the enigmatic nature of dark energy.

• Pathway for Future Research: The theoretical constructs establish a robust foundation for advancing research in cosmology, astrophysics, and particle physics.

Potential Implications:

The findings could influence a wide array of physics subfields, paving the way for exploring antigravitational effects, particle behaviour near the speed of light, and the evolution of matter under extreme conditions.

While experimental validation remains essential, the paper's rigorous mathematical and theoretical underpinnings mark it as a significant contribution to the field of physics, opening new horizons for discovery and innovation.

#NegativeApparentMass, #MatterMassTransition, #AntigravityEffects, #EffectiveMassDynamics,

Time error is incorrectly represented as time dilation:

Subject: Clarifying Oscillation, Clock Rate, and Time Dilation Misconceptions

Dear Mr. Phillips,

I appreciate your engagement with my work, Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. However, your comments introduce conceptual inaccuracies and misinterpretations that require clarification. Allow me to address your points systematically:

1. Oscillation Is Not Synonymous with Clock Rate

Your reference to “oscillation” as “matter’s clock rate” is an arbitrary and non-standard description. While oscillations can indeed describe periodic motion, not all oscillations qualify as clock oscillations.

Standardized Clock Oscillations:

A clock oscillation is carefully engineered to maintain regular periodicity under specific conditions. Standardized clocks are designed to represent time accurately on a 360∘ time scale, specific to a particular location and environmental conditions.

External Influences and Error:

Deviation from standardized oscillation due to influences such as gravitational potential, temperature, or speed results in an error in time measurement, not a universal effect such as time dilation.

2. Misconception About Oscillation in Gravitational Fields

You stated: “Oscillation has been proven to be slower in regions nearer to a gravitational mass.”

This is incorrect. In fact:

Faster Oscillation Closer to a Gravitational Mass:

Clocks nearer to a gravitational well experience stronger gravitational influences, which increase the oscillator’s mechanical deformation and can result in faster oscillations. However, lower gravitational potential energy causes deviations from proper time, which are observed as errors in time measurement, not genuine time dilation.

Not Time Dilation, but Error in Time:

Proper time (t) on a 360∘ scale is defined within the framework of standardized clocks. The concept of time dilation (t′), as postulated by special relativity, stipulates t′>t. Since t′ exceeds the 360∘ scale of proper time, any deviation observed within a clock mechanism arises from errors induced by external influences, not a physical dilation of time itself.

3. Understanding Time Error Through Mechanical Deformation

External forces affecting a clock mechanism, such as gravitational potential differences, cause mechanical deformation in oscillatory components, like piezoelectric oscillators. This phenomenon can be explained using classical mechanics, specifically Hooke’s law. Such errors are well-documented and differ fundamentally from the relativistic interpretation of time dilation.

4. Special Relativity Misinterprets Errors as Time Dilation

The concept of time dilation in special relativity is invalidated when the phase shift in oscillatory frequencies is rigorously analysed. As outlined in my research, Relativistic Effects on Phase Shift in Frequencies Invalidate Time Dilation, the relativistic claim conflates mechanical errors with a universal effect on time itself.

I invite you to consult this research for a detailed analysis:

Relativistic Effects on Phase Shift in Frequencies Invalidate Time Dilation

5. Addressing Future Comments

I encourage you to refer to the above research and my arguments before making further comments related to time dilation. A clear understanding of these concepts will help you engage meaningfully with the objectives of my work.

In Summary:

Oscillation and clock rate are not universally interchangeable terms.

Errors in time readings arise from external influences, not a fundamental dilation of time.

Relativity’s time dilation misrepresents localized mechanical errors as universal phenomena.

I hope this clarifies your misconceptions. I remain open to productive discussions that align with the research's scope and objectives.

Best regards,

Soumendra Nath Thakur

Electromagnetic Wave: Constant Effective Acceleration and Antigravitational Force

Soumendra Nath Thakur

ORCiD:0000-0003-1871-7803

November 30,2024

Abstract

This study presents the determination of the constant effective acceleration (aᵉᶠᶠ) and the associated force (Fₚₕₒₜₒₙ) experienced by electromagnetic waves, specifically photons, within the framework of Extended Classical Mechanics. The photon’s motion is analysed based on the distance travelled in one second, under the assumption of constant acceleration. The analysis reveals a constant effective acceleration of 6 × 10⁸ m/s², producing a negative effective force due to the negative apparent mass (Mᵃᵖᵖ) of the photon, exhibiting an antigravitational effect. This elucidates the interaction dynamics of photons in gravitational fields.

Keywords: Constant effective acceleration, antigravitational force, photons, Extended Classical Mechanics, apparent mass, electromagnetic waves.

Elucidation

Determination of Constant Effective Acceleration

The motion of photons is described using the equation for constant acceleration:

Δd = v₀Δt + (1/2)aᵉᶠᶠ(Δt)²

Where:

• Δd = Distance travelled by the photon (3 × 10⁸ m), 
• v₀ = Initial velocity (0m/s at emission),
• Δt = Time interval (1 s),
• aᵉᶠᶠ = Effective acceleration to be determined.

Substituting the values:

3 × 10⁸ m = 0·1 s + (1/2)aᵉᶠᶠ(1)²

Solving for aᵉᶠᶠ:

aᵉᶠᶠ =  6 × 10⁸ m/s²

Effective Force Acting on Photons

The force experienced by photons arises from their effective mass (Mᵉᶠᶠ = −Mᵃᵖᵖ) and is given by:

Fₚₕₒₜₒₙ = −Mᵃᵖᵖ·aᵉᶠᶠ 

Using the Extended Classical Mechanics force equation, F = (Mᴍ −Mᵃᵖᵖ)·aᵉᶠᶠ = Mᵉᶠᶠ·aᵉᶠᶠ, the terms simplify for photons, as the matter mass Mᴍ = 0,  and velocity v=c:

Fₚₕₒₜₒₙ = −Mᵉᶠᶠ·aᵉᶠᶠ

 

Antigravitational Implications

The negative apparent mass (Mᵃᵖᵖ) results in a negative force, implying an antigravitational interaction. This force opposes the gravitational attraction and contributes to the constant speed of photons, consistent with their behaviour in gravitational fields.

Conclusion

Within the framework of Extended Classical Mechanics, the interaction of electromagnetic waves, such as photons, with gravitational fields reveals:

1. A constant effective acceleration aᵉᶠᶠ = 6 × 10⁸ m/s²

2. A negative force Fₚₕₒₜₒₙ = −Mᵉᶠᶠ·aᵉᶠᶠ, signifying an antigravitational effect.

This antigravitational force is a direct consequence of the negative apparent mass of photons, offering a deeper understanding of their motion and interaction in gravitational environments.

#Constanteffectiveacceleration, #antigravitationalforce, #photons, #ExtendedClassicalMechanics, #apparentmass, #electromagneticwaves,

Revisiting De Broglie’s Pilot Wave Theory: Mass, Force Dynamics, and the Wave Behaviour of Particles.

Soumendra Nath Thakur

November 29, 2024

Louis de Broglie famously proposed that the movement of matter particles, such as electrons and atoms, is guided by a "quantum wave," thereby explaining their observed wave-like behaviour. However, this interpretation presents significant challenges, particularly when distinguishing between subatomic particles with mass and those that are massless.

On the one hand, subatomic particles like electrons possess a nonzero rest mass (mₑ = 9.1093837 × 10⁻³¹ kg), representing an invariant and intrinsic property. Conversely, massless particles such as photons have a rest mass of m₀ = 0. This fundamental difference has profound implications for their respective dynamics under the framework of extended classical mechanics:

1. For electrons (rest mass >0):

The force equation under extended classical mechanics is given by:

F = (Mᴍ −Mᵃᵖᵖ)·aᵉᶠᶠ 

where Mᴍ = mₑ is the rest mass, Mᵃᵖᵖ is the apparent mass, and Mᵉᶠᶠ = (Mᴍ −Mᵃᵖᵖ) is the effective mass. For electrons, Mᵉᶠᶠ>0, leading to a positive force aligned with the external gravitational force, ensuring their motion follows the classical gravitational influence.

2. For photons (rest mass =0):

The force equation simplifies to:

F = −Mᵉᶠᶠ·aᵉᶠᶠ, 

since Mᴍ = 0 and Mᵉᶠᶠ = −Mᵃᵖᵖ. Here, Mᵉᶠᶠ <0, resulting in a negative force that opposes the direction of the external gravitational force.

Conclusion:

Equations (1) and (2) highlight that the behaviour of subatomic particles is intrinsically tied to their rest mass. For particles like electrons or atoms (rest mass >0), their motion is governed by a positive force in alignment with gravitational attraction. In contrast, massless particles like photons (rest mass =0) are governed by a negative force, which counteracts gravitational pull and points in the opposite direction.

The effective mass for particles with rest mass >0 (e.g., electrons) remains positive, while for massless particles like photons, the effective mass is negative. This difference in force dynamics undermines the notion that matter particles such as electrons or atoms can be accurately described by a "quantum wave." Their positive gravitationally bound force does not account for their wave-like behaviour. Conversely, photons, governed by an antigravitational negative force, are intrinsically linked to "quantum waves," which fully explains their wave-particle duality.

This analysis reveals a fundamental limitation in De Broglie's pilot wave theory. While it successfully explains the dynamics of photons, its application to massive particles like electrons or atoms may not adequately capture their behaviour, challenging the universality of his quantum wave framework.

#QuantumWaveDynamics #EffectiveMass #WaveParticleDuality

A Nuanced Perspective on Dark Energy: Extended Classical Mechanics

Soumendra Nath Thakur

November 27, 2024

Abstract

This study presents an advanced extension of classical mechanics to examine photon dynamics and its parallels with cosmological phenomena, particularly dark energy. Central to this framework is the concept of effective mass (Mᵉᶠᶠ), a dynamic property uniting rest mass (Mᴍ) and apparent mass (Mᵃᵖᵖ). For photons, which have zero rest mass, their apparent mass dictates their energy-momentum exchanges and response to forces, culminating in the reformulated force equation: F = −Mᵃᵖᵖaᵉᶠᶠ.

 

The study reinterprets Newton’s law of gravitation by integrating effective mass, allowing for ground breaking scenarios where negative apparent mass yields negative gravitational mass when −Mᵃᵖᵖ. This phenomenon echoes the behaviour of dark energy (Mᴅᴇ<0), which accelerates the universe's expansion by generating antigravitational effects.

By linking photon dynamics and dark energy, this study unveils a shared mechanism: negative effective mass. This revelation provides a unifying perspective on the interplay between energy and momentum across quantum and cosmological scales, paving the way for a cohesive understanding of gravitational dynamics and fundamental forces.

This nuanced exploration of photon dynamics offers significant insights for understanding the force of antigravity caused by dark energy, even when dark energy remains physically imperceptible and elusive. By extending classical mechanics to incorporate dynamic mass properties, this framework enables better mathematical modelling of the enigmatic force driving cosmic acceleration.

By bridging classical and quantum mechanics with cosmological frameworks, this study deepens our understanding of gravitational interactions and lays the groundwork for future research into the universe’s fundamental workings. The cohesive interpretation of negative effective mass presented here encourages interdisciplinary exploration, with profound implications for unravelling the mysteries of dark energy and its role in shaping the cosmos.

The extended classical mechanics framework thus opens pathways for new theoretical explorations, offering a cohesive mechanism to reconcile classical, quantum, and cosmological phenomena, with implications for deciphering the universe's fundamental forces.

Keywords:

Extended Classical Mechanics, Photon Dynamics, Effective Mass, Apparent Mass, Dark Energy, Gravitational Dynamics, Antigravity Force, Cosmic Acceleration, Negative Gravitational Mass, Quantum Scale Dynamics, Cosmological Models, Energy Momentum Interplay, Force Dynamics, Photon Energy Interactions, Gravitational Fields, Unified Physics Framework, Dark Matter Analogy, Quantum and Cosmological Bridges, Gravitational Lensing, Mathematical Modelling of Dark Energy,

Soumendra Nath Thakur

ORCID iD: 0000-0003-1871-7803

Tagore’s Electronic Lab, West Bengal, India

Correspondence: 

postmasterenator@gmail.com, postmasterenator@telitnetwork.in

Declaration:

Funding: No specific funding was received for this work.

Potential competing interests: No potential competing interests to declare.

_________________

Introduction

The interplay of photons, gravitational dynamics, and cosmic expansion represents a frontier in physics, where classical mechanics encounters its limitations. This study extends classical mechanics by introducing the dynamic concept of effective mass (Mᵉᶠᶠ), combining rest mass (Mᴍ) and apparent mass (Mᵃᵖᵖ) to explore force dynamics in photons and their broader implications. For photons, whose rest mass is zero, the apparent mass governs interactions, leading to the reformulated force equation: F = −Mᵃᵖᵖaᵉᶠᶠ

This framework allows for scenarios involving negative effective mass, drawing analogies with dark energy (Mᴅᴇ<0), which drives the universe's accelerated expansion. By reinterpreting gravitational laws and examining the role of dynamic mass properties, the study connects quantum phenomena like photon dynamics with cosmological forces shaping the cosmos.

This nuanced exploration of photon dynamics offers significant insights for understanding the force of antigravity caused by dark energy, even when dark energy remains physically imperceptible and elusive. By extending classical mechanics to incorporate dynamic mass properties, this framework provides a pathway for better mathematical modelling of the enigmatic force driving cosmic acceleration.

By bridging classical and quantum mechanics with cosmological frameworks, this study not only deepens our understanding of gravitational dynamics but also lays the groundwork for future research on the fundamental interactions shaping the universe. The cohesive interpretation of negative effective mass presented here encourages interdisciplinary exploration, with potential implications for unravelling the mysteries of dark energy and its role in the evolution of the cosmos.

Methodology

This study employs the extended classical mechanics framework to analyse photon dynamics and its implications for gravitational interactions and cosmological phenomena. The methodology involves:

1. Conceptual Foundation:

• Define effective mass (Mᵉᶠᶠ) as the sum of the combined rest mass (Mᴍ) and apparent mass (Mᵃᵖᵖ), emphasizing its dynamic nature.

• Examine apparent mass as a property arising from energy-momentum exchanges, particularly in systems like photons, where Mᴍ=0.

2. Force Dynamics on Photons:

• Derive the force equation F = −Mᵃᵖᵖaᵉᶠᶠ for photons using effective mass and associated acceleration.

• Explore how this equation governs the photon’s motion under varying energy-momentum conditions.

• The derivation of the effective acceleration aᵉᶠᶠ aligns with the methodological exploration of force and acceleration acting on photons. It would complement the discussion of the force equation F = −Mᵃᵖᵖaᵉᶠᶠ and further clarify the dynamics of photons as analysed through the extended classical mechanics framework. The constant effective acceleration: aᵉᶠᶠ = 6 × 10⁸ m/s².

3. Reinterpretation of Gravitational Law:

• Modify Newton’s law of gravitation to incorporate effective mass, enabling scenarios where negative apparent mass leads to altered gravitational interactions.

4. Dark Energy Analogy:

• Establish parallels between the negative effective mass of photons and that of dark energy (Mᴅᴇ<0), which drives cosmic acceleration.

Compare energy-momentum dynamics in photon systems and large-scale cosmological models.

5. Implications:

• Analyse how the extended framework bridges classical mechanics with quantum and cosmological phenomena, providing insights into the interplay of negative effective mass across different physical scales.

Mathematical Presentation:

A Nuanced Perspective on Dark Energy

In the framework of extended classical mechanics, the concept of effective mass (Mᵉᶠᶠ) is pivotal, representing the net mass governing the dynamics of a system. This mass incorporates both the rest mass and dynamic energy-dependent properties, such as the apparent mass (Mᵃᵖᵖ). Apparent mass arises from the energy and momentum characteristics of a photon and is inherently dynamic, distinguishing it from static rest mass. This approach combines theoretical derivations with analogical reasoning to propose a unified view of energy-momentum exchanges in diverse physical systems.

Determination of Constant Effective Acceleration of Photons

The distance travelled by the photon in 1 second is 3 × 10⁸ m, and that the acceleration is constant. The expression for the distance travelled in the case of constant acceleration is given by: 

Δd = v₀Δt + (1/2)aᵉᶠᶠ(Δt)²

Where:

• Δd is the distance travelled (3 × 10⁸ m in 1 second), 

• v₀ is the initial velocity (0 m/s, at emission), 

• Δt is the time (1 second),

• aᵉᶠᶠ is the effective acceleration, which we want to solve for.

Substituting the known values into the equation:

3 × 10⁸ m = 0·1 s + (1/2)aᵉᶠᶠ(1)²

aᵉᶠᶠ =  6 × 10⁸ m/s²

The Force Term:

The equation −Mᵃᵖᵖaᵉᶠᶠ ≠ 0, which implies that there is an effective force acting on the photon due to its apparent mass Mᵃᵖᵖ. The effective force acting on the photon will be related to the effective mass and acceleration by:

F = −Mᵃᵖᵖaᵉᶠᶠ 

Since aᵉᶠᶠ ≠ 0 and Mᵃᵖᵖ is not zero, the force is indeed non-zero, and the photon experiences this force as it accelerates to its constant speed.

Conclusion:

The constant effective acceleration of the photon, based on the distance travelled by photon in 1 second is: 

aᵉᶠᶠ = 6 × 10⁸ m/s².

Extended Classical Mechanics Framework

To examine the force dynamics acting on a photon, we utilize the extended classical mechanics framework. In this system, the force (F) is determined by the photon's effective mass (Mᵉᶠᶠ) and its associated acceleration (aᵉᶠᶠ). The general expression for the force is:

F = (Mᴍ −Mᵃᵖᵖ)·aᵉᶠᶠ = Mᵉᶠᶠ·aᵉᶠᶠ 

Here, Mᴍ represents the rest mass (or matter mass), which for a photon is zero, while Mᵃᵖᵖ denotes the dynamic apparent mass derived from energy-momentum interactions. For a photon, where Mᴍ=0, this equation simplifies to:

F = −Mᵉᶠᶠ·aᵉᶠᶠ

 

This formulation enables the calculation of a photon's response to forces, revealing how its energy and momentum exchanges dictate its motion.

Additionally, the effective mass is expressed as:

Mᵉᶠᶠ = Mᴍ −Mᵃᵖᵖ

Reinterpretation of Newton's Law of Universal Gravitation

The concept of effective mass allows for a reinterpretation of Newton’s law of gravitation. Traditionally, the gravitational force is given by:

Fɢ = G·(Mɢ·M₂)/r²

By substituting Mɢ with Mᵉᶠᶠ , which integrates combined rest mass (Mᴍ) and apparent mass (Mᵃᵖᵖ):

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

When the magnitude of −Mᵃᵖᵖ exceeds that of Mᴍ, the effective gravitational mass (Mɢ) becomes negative, significantly altering gravitational interactions.

Analogies Between Effective Mass and Dark Energy

In cosmology, dark energy is theorized to possess a negative effective mass (Mᴅᴇ<0), creating a repulsive force responsible for the universe's accelerated expansion. Drawing an analogy between dark energy and photons reveals intriguing similarities. Specifically, the equation:

Mᴅᴇ = Mᵉᶠᶠ = Mᴍ − Mᵃᵖᵖ

demonstrates that under certain conditions, both systems can exhibit negative effective mass. This shared property underscores profound implications for their respective roles in the universe.

Just as dark energy shapes the large-scale structure and expansion of the cosmos, the negative effective mass of photons may influence the behaviour of light in gravitational fields, quantum systems, and high-energy environments. This analogy offers a unified perspective on energy-momentum exchanges across quantum and cosmological domains.

Implications

This exploration opens new pathways for understanding the interplay between classical and quantum mechanics and their intersections with cosmological phenomena such as dark energy and gravitational dynamics. By extending classical mechanics to incorporate dynamic mass properties, this framework could bridge gaps between micro- and macro-scale physical theories, providing fresh insights into the fundamental workings of the universe.

Discussion

The extended classical mechanics framework introduces a transformative perspective on the interplay between energy, momentum, and mass, particularly in the context of photons. By incorporating the dynamic concept of apparent mass (Mᵃᵖᵖ), this framework shifts away from static interpretations of mass in classical physics, offering a more comprehensive understanding of force and motion. The effective mass (Mᵉᶠᶠ), which integrates rest mass and apparent mass, redefines gravitational interactions and allows for scenarios involving negative gravitational mass—a concept previously confined to theoretical extremes like dark energy.

This nuanced exploration of photon dynamics offers significant insights into the force of antigravity caused by dark energy, even when dark energy remains physically imperceptible and elusive. The analogy between the negative effective mass of photons and the cosmological behaviour of dark energy reveals a shared mechanism underpinning phenomena such as cosmic acceleration and light propagation. This bridging of quantum-scale dynamics with cosmological models not only elucidates the photon's role in gravitational fields but also provides a pathway for better mathematical modelling of the enigmatic force driving cosmic acceleration.

By extending classical mechanics to incorporate dynamic mass properties, this framework deepens our understanding of gravitational dynamics and lays the groundwork for interdisciplinary exploration. The cohesive interpretation of negative effective mass encourages connections between classical, quantum, and cosmological physics, paving the way for theoretical and experimental investigations into the fundamental interactions shaping the universe. With profound implications for unravelling the mysteries of dark energy, this study highlights the potential of effective mass dynamics as a unifying factor across scales, bridging gaps between micro- and macro-physical phenomena.

Conclusion

This study extends classical mechanics by incorporating the dynamic concept of effective mass (Mᵉᶠᶠ), which integrates combined rest mass (Mᴍ) and apparent mass (Mᵃᵖᵖ), to analyse force dynamics in photons and its cosmological implications. Key findings include:

1. Photon Dynamics:

For photons (Mᴍ=0), the force is governed by their apparent mass and acceleration (F = −Mᵃᵖᵖaᵉᶠᶠ), providing a framework to calculate their responses to energy-momentum exchanges.

2. Gravitational Reinterpretation:

By substituting effective mass into Newton's law of gravitation, scenarios involving negative gravitational mass are explored, revealing altered gravitational interactions when −Mᵃᵖᵖ >Mᴍ.

3. Cosmological Parallels:

The negative effective mass of photons mirrors the behaviour of dark energy (Mᴅᴇ<0), which drives the universe's accelerated expansion. This analogy connects quantum-scale photon interactions with large-scale cosmic phenomena.

Implications:

This nuanced exploration of photon dynamics offers significant insights for understanding the force of antigravity caused by dark energy, even when dark energy remains physically imperceptible and elusive. By extending classical mechanics to incorporate dynamic mass properties, this framework provides a pathway for better mathematical modelling of the enigmatic force driving cosmic acceleration.

By bridging classical and quantum mechanics with cosmological frameworks, this study not only deepens our understanding of gravitational dynamics but also lays the groundwork for future research on the fundamental interactions shaping the universe. The cohesive interpretation of negative effective mass presented here encourages interdisciplinary exploration, with potential implications for unravelling the mysteries of dark energy and its role in the evolution of the cosmos.

References 

[1] Chernin, A. D., Бисноватый-коган, Г. С., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781

[2]Classical Mechanics, by Herbert Goldstein in the Journal of the Franklin Institute, 250 (3), 1950, doi:10.1016/0016-0032(50)90712-5

[3] Modern Physics by Kenneth S. Krane

[4]Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. https://doi.org/10.20944/preprints202409.1190.v3 

[5]Thakur, S. N. (2024) Photon Dynamics in extended classical mechanics: Effective mass, negative inertia, momentum exchange and analogies with Dark Energy. doi:10.20944/preprints202411.1797.v1

[6]Thakur, S.N. (2024) A symmetry and conservation framework for photon energy interactions in gravitational fields. doi:10.20944/preprints202411.0956.v1

[7]Thakur, S.N. (2024) Photon interactions with external gravitational fields: True cause of gravitational lensing. doi:10.20944/preprints202410.2121.v1.