Apparent Weight in the Context of Extended Classical Mechanics:

Apparent weight (Wᵃᵖᵖ) is the perceived lightness or heaviness of an object, shaped by the interplay between its matter mass and effective mass within the surrounding environment. In regions with strong gravitational potential energy but minimal or no external gravitational force, the object’s effective mass can reduce its apparent weight or even make it seem weightless. This happens because the gravitational environment alters how the object’s mass interacts with external forces, potentially making the object appear lighter due to the negative value of apparent mass or as though it’s being pushed upward due to the effect of negative effective mass. Thus, apparent weight reflects not only the force of gravity but the combined effects of the object’s matter mass, its effective mass influenced by apparent mass, the surrounding gravitational field, and any other external forces acting on it.

The apparent weight can also be influenced by the object’s motion. When moving upward, the object can feel heavier due to the opposing force needed to overcome gravity. In contrast, when in free fall, the object experiences weightlessness, as the forces acting on it, including gravity, are effectively in balance, and there is no contact force to give the sensation of weight.

The apparent weight (Wᵃᵖᵖ) can be expressed dynamically as:

 Wᵃᵖᵖ = Mᵉᶠᶠ⋅gₑₓₜ

Where gₑₓₜ is the weak external gravitational acceleration, and (Mᵉᶠᶠ) is the effective mass, which includes a negative component due to the negative apparent mass (Mᵃᵖᵖ):

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

Where Mᵉᶠᶠ includes both matter mass and apparent mass contributions.

Classical Mechanical interpretation of apparent weight:

However, the interpretation of apparent weight within the framework of extended classical mechanics introduces a redefined and expanded perspective. Here, apparent weight is not merely the perceived weight of an object, as described in classical mechanics, but a dynamic property shaped by the interaction between matter mass and effective mass, influenced by negative apparent mass. 

This interpretation diverges from the classical view, which attributes apparent weight solely to the imbalance between gravitational force and contact force. For instance, in classical mechanics, an object submerged in water has an apparent weight equal to its actual gravitational force minus the buoyant force exerted by the fluid. 

In contrast, extended classical mechanics redefines apparent weight as a dynamic property shaped by the gravitational environment and external forces that influence an object's effective mass. This framework introduces a more nuanced understanding of apparent weight under varied conditions—such as strong gravitational potentials or near-weightless states—by accounting for the combined effects of matter mass (Mᴍ) and negative apparent mass (Mᵃᵖᵖ). Unlike classical mechanics, which attributes apparent weight merely to the subtraction of contact force from gravitational force, extended classical mechanics emphasizes the role of effective mass (Mᵉᶠᶠ), providing a richer explanation for weight dynamics beyond classical interpretations.

Soumendra Nath Thakur
ORCiD:0000-0003-1871-7803
November 26, 2024 

#ApparentWeight

My reply to the ResearchGate discussion 'Photon Dynamics: The equation F = −Mᵃᵖᵖ·aᵉᶠᶠ.'

ResearchGate Discussion Photon Dynamics: The equation F = −Mᵃᵖᵖ·aᵉᶠᶠ.

26 November, 2024

Dear Researcher André Michaud,

Thank you for your thoughtful and insightful reply to my discussion post regarding the equation Fₚₕₒₜₒₙ = Mᵉᶠᶠ·aᵉᶠᶠ and its application to photon dynamics in gravitational fields. I deeply appreciate the attention you have drawn to the part of my statement:

"This results in a consistent, negative force propelling the photon away from the gravitational well. Essentially, the photon accelerates from rest to its characteristic speed of light almost instantaneously, driven by this force."

Your reference to de Broglie's conditions published in the 1930s, which require a localized photon to obey Maxwell's equations by being self-propelling and self-guiding in a straight line by default, provides robust theoretical support to my framework. The concept that the photon's self-propelling nature arises from half of its energy propelling the other half is a profound insight that aligns well with the dynamics described in my extended classical mechanics approach.

In particular, your point reinforces the interpretation of the negative force in my equation Fₚₕₒₜₒₙ = Mᵉᶠᶠ·aᵉᶠᶠ, where the photon's total energy (inclusive of its gravitational interaction energy Eg and intrinsic energy E) generates a negative force. This force is critical for the photon's:

Escape from the Gravitational Well: Enabling the photon to overcome the gravitational pull and propagate outward.

Maintenance of Constant Speed (c): Allowing the photon to self-propel and maintain its characteristic speed irrespective of external influences.

The connection you have drawn to de Broglie's hypothesis not only strengthens the theoretical basis of my work but also highlights the consistency between classical mechanics extensions and quantum-mechanical principles. This intersection is invaluable for advancing our understanding of photon behaviour in gravitational contexts and its broader cosmological implications.

I am also intrigued by your reference to your article, "De Broglie’s Double-Particle Photon (Expanded republication PI)," which delves into the energy dynamics and the mechanical aspects of photon properties. I look forward to studying your work further, as it appears to offer significant insights into the photon’s energy circulation and structural dynamics.

Once again, I extend my gratitude for your participation and thoughtful contribution to this discussion. Your support adds depth and rigor to the exploration of photon energy-momentum interactions in gravitational fields and further validates the findings presented in my research.

Best regards,

Soumendra Nath Thakur

Equations that Bridges Extended Classical Mechanics and Quantum Mechanics: Unified Energy Mass Frequency and Effective Mass.

Soumendra Nath Thakur

ORCiD:0000-0003-1871-7803

November, 2024

Unified Energy-Mass-Frequency Equation:

Mᵉᶠᶠ⋅c² = h⋅f = E

This equation bridges extended classical mechanics and quantum theory, presenting a cohesive framework to describe the energy-mass-frequency relationship. It establishes the equivalence of a photon’s relativistic energy, its effective mass-energy, and its quantum electromagnetic energy.

1. Effective Mass (Mᵉᶠᶠ) in Photon Dynamics

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

Mᵉᶠᶠ = Mɢ = Mᴍ −Mᵃᵖᵖ

Where:

• Mᴍ is the matter mass, representing intrinsic mass, which is zero for photons.

• Mᵃᵖᵖ is the negative apparent mass, reflecting the photon's energy in gravitational interactions (Mᵃᵖᵖ = −Mᵉᶠᶠ).

• Mɢ represents gravitational mass, equivalent to Mᵉᶠᶠ in this framework.

The force equation encapsulates this relationship:

Fₚₕₒₜₒₙ = Mᵉᶠᶠ·aᵉᶠᶠ 

This underscores that the photon's behaviour in gravitational fields is dictated by its energy-driven effective mass Mᵉᶠᶠ, not rest mass.

2. The Term Mᵉᶠᶠ⋅c²:

This term represents the effective mass-energy of a photon in extended classical mechanics. While photons lack rest mass (M₀=0), their effective mass Mᵉᶠᶠ emerges from their intrinsic energy (E):

Mᵉᶠᶠ = E/c² = (h⋅f)/c²

By incorporating Mᵉᶠᶠ into the energy equation, we establish that the photon's energy (E) governs mass-like behaviour in gravitational interactions, enabling the photon to exchange momentum and energy dynamically.

3. Quantum Energy: E=h⋅f

This represents the photon's quantum electromagnetic energy, where h is Planck's constant, and f is the frequency.

• It highlights the quantum nature of photons, carrying discrete energy quanta proportional to their frequency.

• In gravitational interactions, the frequency f changes (redshift/blueshift), impacting the energy and effective mass of the photon.

4. Relativistic Energy: 

E=Mᵉᶠᶠ⋅c² 

This term extends Einstein's equation (E=mc²) to photons by substituting the effective mass (Mᵉᶠᶠ) for rest mass.

• Even without rest mass, photons possess energy equivalent to a mass-like quantity due to their motion and frequency, emphasizing the role of effective mass in photon dynamics.

5. Unified Representation

The equation Mᵉᶠᶠ⋅c² = h⋅f = E provides a unified perspective:

• It integrates quantum mechanics (h⋅f) with relativistic energy principles (Mᵉᶠᶠ⋅c²).

• It connects the effective mass (Mᵉᶠᶠ) with electromagnetic frequency (h⋅f), demonstrating the equivalence of relativistic and electromagnetic energy (E).

This unified representation aligns classical mechanics with quantum principles, emphasizing the photon’s dual nature as both a quantum particle and a relativistic entity.

6. Significance in Photon Dynamics

• Energy-Mass Interplay:

The inclusion of Mᵉᶠᶠ emphasizes its pivotal role in gravitational interactions. Despite photons lacking rest mass, their effective mass enables them to interact gravitationally.

• Observable Phenomena:

Gravitational lensing, redshift, and energy exchanges are explained through momentum transfer facilitated by Mᵉᶠᶠ. 

• Force Dynamics:

The force equation Fₚₕₒₜₒₙ = Mᵉᶠᶠ·aᵉᶠᶠ represents the negative force generated by the photon’s total energy, which includes both its gravitational interaction energy (Eg) and its intrinsic energy (E). This negative force is responsible for:

Escape from the Gravitational Well: 

Facilitating the photon’s ability to escape the gravitational pull of the source well by expending energy associated with its gravitational interaction (Eg).

Maintenance of Constant Speed (c): 

Sustaining the photon’s constant speed by utilizing the negative force generated from its inherent energy (E), which is not expended unless there is cosmic recession.

By expressing E as both Mᵉᶠᶠ and h⋅f, this framework integrates the principles of classical mechanics and quantum mechanics, providing a unified model for photon behaviour in gravitational fields. Rather than relying on geometric spacetime curvature, this approach introduces quantifiable energy-mass-frequency relationships, advancing the understanding of photon dynamics.

#ECM #EffectiveMass #ForceEquation #UnifiedEquation #UnifiedEnergyMassFrequency #UnifiedEnergy #UnifiedMass #UnifiedFrequency

Extended Classical Mechanics: Unified Energy-Mass-Frequency Equation.

Soumendra Nath Thakur

ORCiD:0000-0003-1871-7803

November, 2024

Unified Energy-Mass-Frequency Equation:

Mᵉᶠᶠ⋅c² = h⋅f = E

This equation bridges the principles of classical mechanics and quantum theory, presenting a unified framework for understanding the energy-mass-frequency relationship in the context of photon dynamics. It establishes the equivalence between the relativistic energy of a photon, its effective mass-energy, and its quantum electromagnetic energy.

1. The Term Mᵉᶠᶠ⋅c²:

Represents the effective mass-energy of a photon derived from the extended classical mechanics framework.

While photons have zero rest mass (M₀=0), their effective mass Mᵉᶠᶠ is nonzero, as it emerges from their intrinsic energy E.

This term expresses how the photon's energy relates to mass-like behaviour when interacting with gravitational fields, making it pivotal in explaining photon dynamics without invoking spacetime curvature.

2. The Energy E=h⋅f:

Describes the quantum electromagnetic energy of a photon, where h is Planck’s constant and f is the photon's frequency.

This component reflects the quantum nature of photons as particles of light, carrying discrete energy quanta proportional to their frequency.

3. The Energy  E = Mᵉᶠᶠ⋅c²:

Conveys the relativistic energy equivalence, extending Einstein’s E=mc² to photons by replacing rest mass with effective mass.

This shows that photons, despite having no rest mass, possess energy equivalent to a mass-like quantity due to their motion and frequency.

4. Unified Representation:

This equation unifies the concepts of classical mechanics and quantum mechanics by demonstrating that the energy of a photon can be equivalently described through its effective mass (Mᵉᶠᶠ), relativistic principles (c²), and its electromagnetic frequency (h⋅f).

It reflects a seamless connection between classical and quantum perspectives, supporting the broader framework of extended classical mechanics.

Significance in Photon Dynamics:

This relationship underscores how photons interact with gravitational fields, with their effective mass enabling energy and momentum exchanges that result in observable phenomena such as gravitational lensing and redshift. By expressing E as both h⋅f and Mᵉᶠᶠ⋅c², this equation highlights the dual nature of photons as quantum particles and relativistic entities, emphasizing their dynamic role in gravitational systems.

#ECM #UnifiedEquation #UnifiedEnergyMassFrequency #UnifiedEnergy #UnifiedMass #UnifiedFrequency

Extended Classical Mechanics: Effective Mass (Mᵉᶠᶠ) in Force Equation.

Soumendra Nath Thakur

ORCiD:0000-0003-1871-7803

November, 2024

In the framework of extended classical mechanics, the force equation is expressed as:

F = Mᵉᶠᶠ·aᵉᶠᶠ 

where Mᵉᶠᶠ represents the effective mass and aᵉᶠᶠ is the effective acceleration. The term Mᵉᶠᶠ encapsulates the combined contributions of the gravitational mass Mɢ, matter mass Mᴍ, and the negative apparent mass Mᵃᵖᵖ:

Mᵉᶠᶠ = Mɢ = Mᴍ −Mᵃᵖᵖ

Key Components of Mᵉᶠᶠ:

1. Matter Mass (Mᴍ):

The intrinsic mass of the particle or system derived from its rest energy and other inherent properties. For photons, this is zero (Mᴍ=0), emphasizing the absence of rest mass.

2. Negative Apparent Mass (Mᵃᵖᵖ):

A novel concept introduced in this framework, representing the effect of the photon's energy in gravitational interactions. For photons, Mᵃᵖᵖ is directly proportional to their energy, defined as:

Mᵃᵖᵖ = −Mᵉᶠᶠ

3. Gravitational Mass (Mɢ):

In this extended theory, gravitational mass is redefined to include the interplay between matter mass and negative apparent mass, making it an equivalent term for effective mass (Mᵉᶠᶠ).

Role of Mᵉᶠᶠ in the Force Equation:

The force F arises from the interaction between the effective mass (Mᵉᶠᶠ) and the effective acceleration (aᵉᶠᶠ) experienced by a particle or photon in a gravitational and anti-gravitational fields.

For photons, Mᴍ=0, and the effective mass is entirely attributed to the interplay of energy and gravitational potential through Mᵃᵖᵖ. This highlights the unique dynamics of massless particles like photons under gravitational influences.

#ECM #EffectiveMass #ForceEquation