Discussion
Started 30 August 2024
  • Tagore's Electronic Lab.

Dark Energy as a By-Product of Negative Effective Mass: Discussion.

Soumendra Nath Thakur
31-08-2024
Effective dark energy is interpreted as a manifestation of negative effective mass, a concept rooted in extended classical mechanics and involving the dynamics of potential, kinetic, and gravitational forces. This phenomenon emerges from the apparent reduction in invariant matter mass and its resulting influence on the universe's overall dynamics.
Note: Matter mass Mᴍ is understood as the combined mass of normal matter (such as baryonic matter) and dark matter.
Summary:
Effective dark energy, considered a by-product of negative effective mass, arises from the intricate interplay of potential, kinetic, and gravitational dynamics in the universe. This concept challenges traditional views by suggesting that dark energy is not a separate entity but rather a consequence of negative effective mass. The fundamental equation, PEᴛₒₜᴜₙᵢᵥ ∝ Mᵉᶠᶠᴜₙᵢᵥ, establishes a direct relationship between the universe's potential energy and its effective mass, highlighting their intrinsic connection.
In the early universe, effective mass played a critical role in determining the potential energy. The universal force was necessary to convert this potential energy into kinetic energy, facilitating the rapid expansion of the universe. As the effective mass decreased, acceleration increased, reflecting the dynamics of this early rapid expansion, as described by the equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ. This equation illustrates that the universal force is directly proportional to effective acceleration, offering key insights into the universe's expansion dynamics.
As the universe continued to evolve, its potential energy became influenced by both matter mass and effective mass, including contributions from dark energy and other effective masses. Later, the universal force was shaped by both matter and effective mass, with effective acceleration inversely related to the combined mass. The ongoing generation of dark energy and its dominance in gravitational dynamics are thus explained by the relationship between effective mass and gravitational effects, suggesting a repulsive gravitational force that significantly influences the universe's structure and evolution.
Effective dark energy can thus be seen as a by-product of negative effective mass, arising from the complex interrelations of potential, kinetic, and gravitational forces, and reflecting the apparent reduction in invariant matter mass over time.
Reference: Chernin, A. D., Bisnovatyi-Kogan, G. S., 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
UPDATE 01-09-2024:
Expanded Insights on Negative Effective Mass and Dark Energy Dynamics
Negative Effective Mass: Insights from Universal Force and Acceleration Dynamics
The universal force Fᴜₙᵢᵥ is defined by the product of the effective acceleration aᵉᶠᶠᴜₙᵢᵥ and the combined inverse contributions of two types of mass: the variable effective mass Mᵉᶠᶠᴜₙᵢᵥ and the constant matter mass Mᴍᴜₙᵢᵥ. This relationship emphasizes that the universal force depends not only on acceleration but also on the dynamic interplay between these masses. The effective mass reflects the system’s response to dynamic factors such as motion and gravitational interactions, and it can differ from the constant matter mass by varying according to system conditions.
The universal force and acceleration increase or decrease proportionally with the combined reciprocal masses, where variations in the effective mass directly influence acceleration and the resulting universal force. As the effective mass decreases, acceleration increases, and vice versa. This relationship aligns with the interpretation of "negative effective mass," where changes in the dynamic state of the universe alter gravitational interactions.
The concept of "negative effective mass" arises from this interpretation of effective mass. When extended to dark energy's influence on gravitational dynamics, it captures the idea that the effective mass may exhibit properties akin to a negative effective density, leading to repulsive gravitational effects. In this context, "negative effective mass" describes how the dynamic properties of dark energy counteract gravitational attraction, contrasting with the attractive behaviour of conventional matter.
The effective mass Mᵉᶠᶠᴜₙᵢᵥ reflects the apparent mass loss or gain relative to the constant matter mass Mᴍᴜₙᵢᵥ. When there is an apparent mass loss, the effective mass increases to maintain balance within the system’s dynamics, suggesting that under certain conditions, the effective mass could be perceived as "negative." This negative value provides a framework for understanding inverse gravitational effects observed with dark energy, where repulsive dynamics challenge traditional gravitational interactions.
Additionally, when the universal force Fᴜₙᵢᵥ increases, the effective acceleration aᵉᶠᶠᴜₙᵢᵥ also increases. Initially, the effective mass Mᵉᶠᶠᴜₙᵢᵥ is equivalent to the matter mass Mᴍᴜₙᵢᵥ. However, as force or acceleration continues to increase, the effective mass can exceed the matter mass, thereby potentially dominating the gravitating mass Mɢᴜₙᵢᵥ. This implies that the effective mass plays a crucial role in determining the overall gravitational behaviour, supporting the idea of "negative effective mass" in scenarios where dark energy exerts a repulsive force.
By incorporating the concept of "negative effective mass" into the extended framework of classical mechanics, we develop a more comprehensive understanding of the gravitational dynamics, allowing us to account for the repulsive effects of dark energy on the universe's expansion. This refined interpretation bridges the abstract notion of dynamic mass variations with observable cosmological phenomena, providing insight into the complex interplay between mass, force, and acceleration in the universe.
Dark energy's influence on the universe's expansion can be understood in terms of the effective mass (Mᵉᶠᶠᴜₙᵢᵥ) exhibiting properties that suggest a negative effective density. When the effective mass exceeds the matter mass (Mᴍᴜₙᵢᵥ), it contributes to gravitational dynamics that may resemble those associated with a negative gravitating mass (Mɢᴜₙᵢᵥ), leading to the repulsive effects observed in the universe.
Mathematical Framework:
The mathematical framework establishes a relationship between potential energy, effective mass, and universal force, providing insight into the universe's expansion and the concept of "negative effective mass." The potential energy of the universe (PEᴛₒₜᴜₙᵢᵥ) is directly proportional to the effective mass (Mᵉᶠᶠᴜₙᵢᵥ), indicating that the effective mass plays a crucial role in defining the universe's dynamics.
The equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ describes the universal force as directly proportional to effective acceleration (aᵉᶠᶠᴜₙᵢᵥ) and inversely proportional to effective mass (Mᵉᶠᶠᴜₙᵢᵥ). An increase in acceleration leads to an increase in the universal force and a corresponding decrease in effective mass, which can lead to the formation of matter. Over time, potential energy becomes dependent on both the matter mass (Mᴍᴜₙᵢᵥ) and the present effective mass, shaping the gravitational dynamics.
By linking these parameters, this framework explains how variations in effective mass, particularly when perceived as negative, contribute to the repulsive effects associated with dark energy, providing a comprehensive view of the complex interplay between mass, force, and acceleration in the universe.
The Equations:
PEᴛₒₜᴜₙᵢᵥ ∝ Mᵉᶠᶠᴜₙᵢᵥ,
This expression, establishes a direct relationship between the universe's potential energy and its effective mass. In the early universe, effective mass played a critical role in determining the potential energy. The universal force was necessary to convert this potential energy into kinetic energy, facilitating the rapid expansion of the universe. As the effective mass decreased, acceleration increased, reflecting the dynamics of this early rapid expansion.
The equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ
describes that the universal force is directly proportional to effective acceleration, and effective acceleration is inversely proportional to effective mass. This relationship suggests that in the early universe, the universal force was the product of the effective mass and the effective acceleration.
Since acceleration is inversely proportional to mass, an increase in effective acceleration leads to a corresponding increase in the universal force, which, in turn, causes a decrease in the effective mass as the acceleration increases, and so corresponding increase in matter mass through formation. As acceleration increase, the effective mass decrease, forming matter mass.
Later, the potential energy became dependent on both the matter mass (Mᴍᴜₙᵢᵥ) and the present effective mass.
The force is influenced by the interaction between the matter mass and the effective mass, where the effective acceleration (aᵉᶠᶠᴜₙᵢᵥ) is inversely related to the total mass, comprising both matter and effective mass, represented by the equation:
Fᴜₙᵢᵥ = (Mᴍᴜₙᵢᵥ+Mᵉᶠᶠᴘᵣₑₛₑₙₜ) · aᵉᶠᶠᴜₙᵢᵥ
As the effective acceleration increases, the apparent matter mass decreases, corresponding increase in present effective mass, which is negative, within this combined mass. Thus, the emergence of dark energy from negative effective mass and its dominant role in gravitational dynamics can be explained by the relationship between effective mass and gravitational effects. As acceleration increased, the apparent matter mass decreased, generating effective mass.
Dark energy's influence on the universe's expansion can be understood in terms of the effective mass (Mᵉᶠᶠᴜₙᵢᵥ) exhibiting properties that suggest a negative effective density. When the effective mass exceeds the matter mass (Mᴍᴜₙᵢᵥ), it contributes to gravitational dynamics that may resemble those associated with a negative gravitating mass (Mɢᴜₙᵢᵥ), leading to the repulsive effects observed in the universe. As provided under, "Negative Effective Mass: Insights from Universal Force and Acceleration Dynamics.

Most recent answer

Time and mass
What is mass?
what is time
Does mass have meaning without the passage of time?
Does any mass fall in a gravitational field without passing time?
Does a magnetic field exist without the passage of time?
exactly...
Time and mass dilation indicate the direct relationship between time and material nature...
If the dimensions of the world are more than three, geodesics are created for movement.
Movement in the dimensions of time...
Time is a geometric potential difference.
And the density is the main reason for the geometry potential difference.
That is, heavier objects move more slowly in time dimensions.
And movement in space reduces movement in the time dimension (time dilation).
Density in the present
Negative density in the past tense
Negative density in the future
This explains the one-way arrow of time.
Negative density can be dark matter and dark energy results from dark matter.
It is the factor of space expansion.
2 Recommendations

All replies (6)

Soumendra Nath Thakur
Tagore's Electronic Lab.
Dear Mr.
Robert A. Phillips
,
Thank you for your questions and comments on my discussion post.
Q: Gravitational waves, including light, are not observable until they interact with the observer.
A: Gravitational waves and light are both forms of energy-carrying propagating waves that travel through a vacuum at a constant speed, which is the speed of light (c). Their detectability depends on the distance between their sources and the detectors and the time taken for their signals to reach the observer. Gravitational waves and light remain undetectable until their signals interact with and are measured by an observer.
Q: Atomic clocks show that falling reduces the internal kinetic energy (potential energy) of matter.
A: The statement "Atomic clocks show that falling reduces the internal kinetic energy (potential energy) of matter" is a bit confusing. Falling itself does not directly reduce internal kinetic energy or potential energy of matter; rather, it affects how potential energy is transformed into kinetic energy as an object moves in a gravitational field. Atomic clocks can measure effects due to gravitational fields, but they do not directly reflect internal energy changes in the way described.
Q: Is there a connection between negative mass and/or dark energy and the changes or disturbances caused by the gravitational effects of falling or orbiting bodies?
A: Based on the research by Chernin et al. in "Dark Energy and the Structure of the Coma Cluster of Galaxies," dark energy is associated with a negative effective mass (Mᴅᴇ). The study introduces three types of mass:
Matter Mass (Mᴍ): This is the total mass of both dark matter and baryonic matter within the Coma Cluster, contributing to its gravitational binding.
Dark Energy Effective Mass (Mᴅᴇ): This conceptual mass represents the effect of dark energy, characterized by negative pressure, resulting in a negative mass (Mᴅᴇ < 0) that counteracts gravitational attraction.
Gravitating Mass (Mɢ): This is the net mass responsible for gravitational attraction, combining the effects of matter mass and dark energy, as expressed by the equation:
  • Mɢ = Mᴍ + Mᴅᴇ
Our research concludes that dark energy and negative apparent mass can be understood as outcomes of gravitational dynamics and motion. This framework extends classical mechanics to explain gravitational interactions, incorporating phenomena associated with dark energy. We characterize dark energy as the universe’s potential energy, linked with a negative effective mass (<0).
We further develop the concept of Negative Apparent Mass (-Mᵉᶠᶠ) based on the negative effective mass of dark energy (Mᴅᴇ) in its current form. According to our model, dark energy’s negative effective mass was the predominant energetic form in the primordial universe. Currently, this negative effective mass (Mᴅᴇ) is regenerated as a result of gravitational dynamics and motion. This regenerated negative effective mass manifests as Negative Apparent Mass in classical mechanics, applicable to both regular and cosmic scenarios.
In extended classical mechanics, we describe the force equation of motion as:
  • F = Mᵉᶠᶠ·aᵉᶠᶠ
where the effective mass Mᵉᶠᶠ includes both matter mass (Mᴍ) and negative apparent mass (-Mᵉᶠᶠ), with:
  • Mᵉᶠᶠ = Mᴍ + (-Mᵉᶠᶠ),
The gravitational equation in extended classical mechanics is:
  • F𝑔 = G·(Mɢ·M₂)/r²,
Where: Mɢ = Mᴍ + Mᵉᶠᶠ
This approach shows that negative apparent mass (-Mᵃᵖᵖ) and the negative effective mass of dark energy (Mᴅᴇ) arise from gravitational dynamics and motion rather than being substances themselves. This reinterpretation aligns with extended classical mechanics principles and provides a coherent framework for understanding gravitational interactions.
In conclusion, there is indeed a significant connection between negative mass and dark energy and the changes or disturbances caused by the gravitational effects of falling or orbiting bodies. The regeneration of negative effective mass of dark energy, as a consequence of gravitational dynamics and motion, affects the observable properties and interactions of these phenomena. Integrating these concepts into classical mechanics helps better understand how such effects manifest in both regular and cosmic contexts.
Best regards,
Soumendra Nath Thakur
Soumendra Nath Thakur
Tagore's Electronic Lab.
Dear Mr.
Robert A. Phillips
,
Thank you for your response concerning falling clocks.
However, the focus of our discussion is "Dark Energy as a By-Product of Negative Effective Mass," and a question about falling clocks is not directly relevant to this topic. Addressing your question on falling clocks might not contribute to the core discussion on Dark Energy and its Negative Effective Mass. I would encourage keeping our conversation focused on the specific topic at hand.
Regarding your statement that a falling clock closer to Earth oscillates more slowly than one at a higher position, leading to a reduction in subatomic kinetic energy proportional to the square of the relative clock rate:
Please note that, scientifically, a clock closer to Earth actually oscillates faster, not more slowly, than one at a higher altitude due to the stronger gravitational force at Earth's surface. This results in a more energetic condition, where higher energy corresponds to a higher frequency and therefore a higher oscillation rate, according to Planck's equation, E = hf.
Your statement seems to touch on how a falling mass under Earth's gravitational force undergoes deformation due to strain, which causes corresponding changes in its dimensions, as explained by Hooke's Law. Furthermore, gravitational force affects the internal subatomic and molecular structure of the falling mass, leading to strain and deformation in accordance with force-mass equations in classical mechanics.
Consequently, the oscillation of the atomic clock is affected, leading to distortion in the clock's time readings. My research paper, titled "Relativistic Effects on Phase Shift in Frequencies Invalidate Time Dilation II," provides a comprehensive explanation and solution to this issue. You can access it at this URL:
This research demonstrates that variations in gravitational forces (G-forces) cause internal particles of matter to interact, resulting in stresses and deformations within the matter. Distortions in wavelength due to phase shifts in relative frequencies directly correspond to time distortions, as described by the relationship λ∝T, where λ represents the wavelength and T the period of oscillation. Relativistic effects, such as differences in speed or gravitational potential, influence the clock's mechanism through phase shifts in frequencies, resulting in increased wavelengths of clock oscillations and subsequent errors in time readings. These phase shifts, linked to an increase in the wavelength of clock oscillations, cause time distortion.
Experiments conducted with piezoelectric crystal oscillators in electronic laboratories have shown that wave distortions correspond to time distortions due to relativistic effects. The time interval T(deg) for a 1° phase shift is inversely proportional to the frequency (f), indicating that a wave corresponds to a time shift.
For example, a 1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds (ps).
• For a 1° phase shift, T(deg) = T/360. Since T=1/f, we have:
1° phase shift = T/360 = (1/f)/360.
• For a wave with a frequency f = 5 MHz, the phase shift (in degrees) can be calculated as:
T(deg)= (1/5,000,000)/360 = 555 ps = Δt.
Thus, for a 1° phase shift in a wave with a frequency of 5 MHz and a wavelength λ = 59.95 m, the corresponding time shift (or time delay) Δt is approximately 555 ps.
Therefore, as a falling clock approaches the Earth's surface, it reverses the magnitude of its deformation, thereby reversing the magnitude of time distortion. The phase shift in the oscillation frequency can be used to calculate the magnitude of this time distortion using the following formula:
• For a 1° phase shift: T(deg) = (1/f)/360 = Δt or,
• For an x° phase shift: Δtₓ = x(1/360f₀)
For more details, please refer to my research paper, "Phase Shift and Infinitesimal Wave Energy Loss Equations," available at this URL:
Best regards,
Soumendra Nath Thakur
Time and mass
What is mass?
what is time
Does mass have meaning without the passage of time?
Does any mass fall in a gravitational field without passing time?
Does a magnetic field exist without the passage of time?
exactly...
Time and mass dilation indicate the direct relationship between time and material nature...
If the dimensions of the world are more than three, geodesics are created for movement.
Movement in the dimensions of time...
Time is a geometric potential difference.
And the density is the main reason for the geometry potential difference.
That is, heavier objects move more slowly in time dimensions.
And movement in space reduces movement in the time dimension (time dilation).
Density in the present
Negative density in the past tense
Negative density in the future
This explains the one-way arrow of time.
Negative density can be dark matter and dark energy results from dark matter.
It is the factor of space expansion.
2 Recommendations

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Dark energy is a result of motion and gravitational dynamics, rather than being a substance.
Discussion
8 replies
  • Soumendra Nath ThakurSoumendra Nath Thakur
1. Dark energy has been a subject of considerable debate since its discovery due to its association with the accelerated expansion of the universe. Traditionally perceived as an unknown force or substance, dark energy is better understood as a by-product of the universe’s dynamic processes, particularly the transformation of potential energy into kinetic energy during and after the Big Bang. This work explores the interconnected roles of gravitational forces, kinetic energy, and apparent negative mass, highlighting that dark energy results from the complex interplay between these elements rather than being an independent substance.
2. Initial State of the Universe and Energy Transformation
Immediately after the Big Bang, the universe's total energy consisted of potential and kinetic components:
Eᴛₒₜ,ᴜₙᵢᵥ = PEᴜₙᵢᵥ + KEᴜₙᵢᵥ
In the earliest moments, the universe was dominated by potential energy, which rapidly approached zero as kinetic energy surged from zero to infinity:
PEᴜₙᵢᵥ: ∞ → 0, KEᴜₙᵢᵥ: 0 → ∞
This energetic shift was driven by gravitational dynamics, where the rapid conversion of potential energy into kinetic energy fuelled the universe’s expansion.
3. Emergence of Dark Energy: A Dynamic Outcome
Dark energy did not pre-exist the universe but emerged from the dynamic interactions between mass, gravity, and kinetic energy. As the universe’s initial potential mass accelerated due to gravitational forces, an apparent negative mass effect arose, which we interpret as dark energy:
Fᴜₙᵢᵥ = (Mᴘᴇ,ᴜₙᵢᵥ - Mᵃᵖᵖ,ᴜₙᵢᵥ)·aᵉᶠᶠ,ᴜₙᵢᵥ
Here, the apparent mass (Mᵃᵖᵖ,ᴜₙᵢᵥ) represents the dynamic influence of dark energy, emerging from the acceleration of potential mass under universal forces.
4. Inverse Relationship Between Potential and Kinetic Energy
The universe’s potential energy is inversely related to its kinetic energy, illustrating the natural balance that dictates cosmic evolution:
PEᴜₙᵢᵥ ∝ 1/KEᴜₙᵢᵥ
This relationship underscores the continuous transformation and reactivation of dark energy as the kinetic energy of the universe’s matter evolves.
5. Dark Energy's Dormancy and Reactivation
Dark energy enters a dormant state when kinetic energy and potential energy achieve equivalence. However, as the universe’s matter mass persists in motion, dark energy reactivates, leading to the accelerated expansion observed today. This cyclical behaviour underscores the transient nature of dark energy:
When PEᴜₙᵢᵥ = KEᴜₙᵢᵥ , Mᵃᵖᵖ = 0
As the universe continues to expand, dark energy becomes dominant once again, reflecting the evolving interplay of mass-energy dynamics.
6. Conclusion
Dark energy is not a fundamental substance but a manifestation of the universe’s dynamic processes. The accelerated expansion is driven by the continuous transformation of kinetic and potential energies, highlighting that dark energy is a consequence of the cosmic gravitational and kinetic interplay. This understanding shifts the perspective from viewing dark energy as an isolated force to recognizing it as an emergent property of the universe’s mass-energy transformations.
Time: A Concrete Entity in Relativity or an Abstract Concept in Broader Scientific Understanding?
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18 answers
  • Soumendra Nath ThakurSoumendra Nath Thakur
In human psychology, time is a conscious experience—a construct reflecting the sequence of existence and events. In cosmology and physical sciences, time is often defined as the indefinite, continuous progression of existence and events in a uniform and irreversible succession, extending from the past, through the present, and into the future. This progression is conceptualized as a fourth dimension that exists above the three spatial dimensions.
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This description suggests that time, in its conventional understanding across various scientific disciplines and human experience, is an abstract concept, not a real, tangible entity. While time provides a framework for understanding the succession of events, it does not have a direct physical existence as space does in three dimensions. Time is often viewed as a hyper-dimensional abstraction—imperceptible and unreachable beyond the three-dimensional spatial realm.
However, relativity challenges this interpretation by treating time as a real entity—integrated with space to form a four-dimensional space-time continuum where time becomes subject to physical modifications, such as time dilation. This relativistic concept implies that time is not only concrete but also malleable under the influence of velocity and gravity, leading to discrepancies with other scientific interpretations that consider time an abstract or imaginary concept.
One of the main contentions is that time dilation, a cornerstone of relativity, effectively violates the standardization of time by presenting it as something dilatable, thereby questioning the uniformity and constancy of time itself. The traditional time scale based on a 360-degree cycle—representing a consistent progression—is disrupted by the relativistic notion of time dilation, which converts abstract time into something perceived as "real" or "natural." This treatment of time also seems to ignore the conscious human experience, which understands time as a subjective, psychological construct.
Furthermore, if time is not directly reachable—being an abstract hyper-dimensional concept—what then is the "time" that a clock measures? Clocks are designed to provide a standardized approximation of cosmic time through calibrated frequency counts, such as the electronic transitions of caesium atoms. However, the physical manifestation of time in clocks is inherently subject to distortions, primarily due to gravitational effects. Gravity affects mass and energy, altering the oscillation rates of clocks and resulting in time distortions. Consequently, even the most accurate atomic clocks require periodic adjustments to compensate for these external influences.
The discrepancy between the "real time" measured by clocks and the "conceptual time" of cosmic progression raises further questions about the nature of time. Clocks, intended to represent a uniform progression of time, must contend with gravitational influences that disrupt this uniformity, necessitating ongoing corrections. This challenges the idea that time is a tangible, concrete entity and supports the view that it remains fundamentally an abstract concept—a conceptual framework through which we interpret the order of existence and events.
In short, while relativistic physics proposes that time is a real entity susceptible to physical modifications like time dilation, this interpretation remains contentious when viewed through the lens of broader scientific understanding. Time appears more consistent with an abstract or imaginary concept, a near-approximate representation that is susceptible to external influences, yet ultimately remains beyond the realm of tangible existence.
Role of Effective Mass and Kinetic Energy:
Discussion
6 replies
  • Soumendra Nath ThakurSoumendra Nath Thakur
Effective mass (Mᵉᶠᶠ) is a quasi-physical concept that explains how various forms of energy, such as dark energy and potential energy, influence gravitational dynamics and classical mechanics. When effective mass is negative, it is directly related to matter mass (Mᴍ): as the effective mass becomes more negative, the 'apparent' matter mass decreases. Conversely, as the kinetic energy increases, the magnitude of the negative effective mass increases (i.e., as Mᵉᶠᶠ becomes more negative), and vice versa.
Equations that Bridges Extended Classical Mechanics and Quantum Mechanics: Unified Energy Mass Frequency and Effective Mass.
Discussion
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  • Soumendra Nath ThakurSoumendra 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, Effective Mass, Force Equation, Unified Equation, Unified Energy Mass Frequency Unified Energy Unified Mass Unified Frequency
Generation of Dark Energy in the Universe:
Discussion
4 replies
  • Soumendra Nath ThakurSoumendra Nath Thakur
1. Dark energy has been a subject of considerable debate since its discovery due to its association with the accelerated expansion of the universe. Traditionally perceived as an unknown force or substance, dark energy is better understood as a by-product of the universe’s dynamic processes, particularly the transformation of potential energy into kinetic energy during and after the Big Bang. This work explores the interconnected roles of gravitational forces, kinetic energy, and apparent negative mass, highlighting that dark energy results from the complex interplay between these elements rather than being an independent substance.
Initial State of the Universe and Energy Transformation
Immediately after the Big Bang, the universe's total energy consisted of potential and kinetic components:
Eᴛₒₜ,ᴜₙᵢᵥ = PEᴜₙᵢᵥ + KEᴜₙᵢᵥ
In the earliest moments, the universe was dominated by potential energy, which rapidly approached zero as kinetic energy surged from zero to infinity:
PEᴜₙᵢᵥ: ∞ → 0, KEᴜₙᵢᵥ: 0 → ∞
This energetic shift was driven by gravitational dynamics, where the rapid conversion of potential energy into kinetic energy fuelled the universe’s expansion.
Emergence of Dark Energy: A Dynamic Outcome
Dark energy did not pre-exist the universe but emerged from the dynamic interactions between mass, gravity, and kinetic energy. As the universe’s initial potential mass accelerated due to gravitational forces, an apparent negative mass effect arose, which we interpret as dark energy:
Fᴜₙᵢᵥ = (Mᴘᴇ,ᴜₙᵢᵥ - Mᵃᵖᵖ,ᴜₙᵢᵥ)•aᵉᶠᶠ,ᴜₙᵢᵥ
Here, the apparent mass (Mᵃᵖᵖ,ᴜₙᵢᵥ) represents the dynamic influence of dark energy, emerging from the acceleration of potential mass under universal forces.
Inverse Relationship Between Potential and Kinetic Energy
The universe’s potential energy is inversely related to its kinetic energy, illustrating the natural balance that dictates cosmic evolution:
PEᴜₙᵢᵥ ∝ 1/KEᴜₙᵢᵥ
This relationship underscores the continuous transformation and reactivation of dark energy as the kinetic energy of the universe’s matter evolves.
Dark Energy's Dormancy and Reactivation
Dark energy enters a dormant state when kinetic energy and potential energy achieve equivalence. However, as the universe’s matter mass persists in motion, dark energy reactivates, leading to the accelerated expansion observed today. This cyclical behaviour underscores the transient nature of dark energy:
When PEᴜₙᵢᵥ = KEᴜₙᵢᵥ , Mᵃᵖᵖ = 0
As the universe continues to expand, dark energy becomes dominant once again, reflecting the evolving interplay of mass-energy dynamics.
Dark energy is not a fundamental substance but a manifestation of the universe’s dynamic processes. The accelerated expansion is driven by the continuous transformation of kinetic and potential energies, highlighting that dark energy is a consequence of the cosmic gravitational and kinetic interplay. This understanding shifts the perspective from viewing dark energy as an isolated force to recognizing it as an emergent property of the universe’s mass-energy transformations.
Why can't a black hole engulf the entire universe? What limits its gravitational reach?
Question
12 answers
  • Soumendra Nath ThakurSoumendra Nath Thakur
Since a singularity has properties that reach infinity, one might assume its gravitational influence is also infinite. When a star collapses into a black hole, its mass is compressed into an extremely small volume, leading to a significant increase in gravitational strength near the singularity. For example, a star with a mass of approximately 3.978 ×10³⁰ kg compressed into a volume of 10⁻⁸ m³ results in a gravitational strength multiplier of 3.978 × 10³⁸. This enormous increase in gravitational strength raises the question: why doesn't this immense gravitational pull extend to engulf the entire universe?
However, several factors limit a black hole's gravitational reach:
1. Distance and Diminishing Influence:
Typically, the gravitational influence of a black hole, like any mass, diminishes with distance. While the gravitational pull is extremely strong near the event horizon, it weakens as one moves farther away. However, with a gravitational strength multiplier of 3.978 ×10³⁸, the black hole could engulf enough matter within its reach and correspondingly increase its gravitational strength further. This suggests that the black hole could potentially extend its gravitational reach indefinitely, challenging the idea of diminishing influence over distance.
2. Cosmic Expansion:
The effect of cosmic expansion is not applicable to a black hole within a galaxy, as dark energy's influence is negligible within galactic scales. A black hole cannot be isolated from a galaxy unless it engulfs the entire galaxy, so cosmic expansion does not apply within this context.
3. Gravitational Boundaries:
While black holes are typically found within galaxies, their gravitational influence near the event horizon is immense. The gravitational boundaries of their host galaxies pose limits, but with a gravitational strength multiplier as high as 3.978 ×10³⁸, the black hole could potentially overcome these boundaries by engulfing enough mass to further increase its gravitational pull indefinitely.
Despite the singularity's extreme gravitational strength near its event horizon and the potential for an ever-increasing gravitational pull, the limits posed by the gravitational boundaries of galaxies and cosmic structures may be challenged by the immense gravitational strength of a black hole, suggesting the possibility of extending its reach indefinitely.

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