Relativistic Energy Increase and Effective Mass: Understanding ΔE = mᵉᶠᶠc²

Summary:

In relativistic physics, the total energy of an object increases with its velocity, transitioning from non-relativistic to relativistic speeds. The increase in energy (ΔE) is due to kinetic energy and can be expressed as:

ΔE = (γ - 1)mc² = mᵉᶠᶠc²

Here, mᵉᶠᶠ is the effective mass associated with the increased energy ΔE, which is not a result of nuclear conversion but a consequence of the object's motion. This perspective aligns with Einstein's mass-energy equivalence (E = mc²) and highlights how energy changes with velocity in special relativity, providing a clear understanding of effective mass in this context.

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

15-04-2024

The summary of the concepts:

E(v ≪ c) < E(v < c): This inequality reflects that the total energy of an object increases as its velocity increases from non-relativistic (v ≪ c) to relativistic speeds (v < c).

E(v < c) − E(v ≪ c) = ΔE: ΔE represents the increase in total energy due to the kinetic energy gained as the velocity increases.

ΔE = mᵉᶠᶠc², where mᵉᶠᶠ is the effective mass associated with ΔE: This equation relates velocity-induced kinetic energy ΔE to an effective mass mᵉᶠᶠ that would correspond to the energy E if converted into mass according to E = mc².

This assertion correctly emphasizes that ΔE is not a result of nuclear conversion but rather a consequence of the object's motion at less than the speed of light c.

This presentation effectively captures the key points regarding energy increase, effective mass, and their relationship in relativistic contexts. It provides a clear understanding of how energy changes with velocity and the concept of effective mass in special relativity.

Let's describe the points clearly:

1. Total Energy E:

In special relativity, the total energy E of an object with rest mass m and velocity v is given by: 

E = γmc² 

where γ = 1/√(1-v²/c²) is the Lorentz factor, c is the speed of light.

2. Delta ΔE:

ΔE represents the change in total energy when the velocity v increases from v≪c to v<c:

ΔE = γmc² - mc² = (γ−1)mc² 

ΔE corresponds to the increase in total energy due to the kinetic energy gained by the object as its velocity increases.

3. Effective Mass mᵉᶠᶠ:

ΔE can be associated with an effective mass mᵉᶠᶠ such that:

ΔE = mᵉᶠᶠc² 

mᵉᶠᶠ​ is the effective mass equivalent to ΔE. It represents the mass that would correspond to the energy ΔE in the context of relativistic energy-momentum relations.

The assertion that ΔE is a consequence of the object's motion relative to the speed of light c, not a result of nuclear processes, aligns with the principles of special relativity. This perspective underscores that ΔE = mᵉᶠᶠc² signifies the manifestation of energy increase due to velocity, clarifying the relationship between kinetic energy and effective mass in relativistic contexts.

This presentation encapsulates the key points regarding energy increase, effective mass, and their interplay within special relativity. It provides a coherent understanding of how energy changes with velocity and the concept of effective mass as defined by relativistic principles, enhancing comprehension beyond traditional Newtonian mechanics.

Advancing Science: Imperatively Refining Theories Through Critical Evaluation.

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

14-04-2024

Refining and discarding flawed or inaccurate aspects of a scientific theory is a crucial part of scientific progress. In fact, it's integral to the scientific method itself, which emphasizes testing hypotheses, scrutinizing evidence, and revising theories based on new discoveries.

When scientists identify inconsistencies, errors, or limitations in a theory, they actively work to address these through rigorous investigation and experimentation. This process can lead to adjustments, refinements, or even paradigm shifts in scientific understanding. Such refinement is aimed at improving the accuracy, predictive power, and explanatory scope of scientific theories.

Therefore, there is no dishonour in critically evaluating and refining theories. On the contrary, it is a testament to the self-correcting nature of science and its commitment to advancing knowledge. By acknowledging and addressing shortcomings, scientists pave the way for deeper insights and more robust theories that better reflect the complexities of the natural world.

Flawed Relativistic Time Dilation is Confirmed by Biased Experiments:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

14-06-2024

Lay Summary

Phase shifts and infinitesimal loss of wave energy occur when an oscillatory wave experiences a change in its phase angle, which can happen due to relativistic effects including interactions with different media or obstacles. Wavelength distortions refer to changes in the wavelength of an oscillatory wave due to phase shifts, as phase shift is inversely proportional to wavelength. These can occur due to various factors, excluding dispersion or refraction, as propagating waves are different than oscillatory waves.

Time dilation is a flawed concept in Einstein's theory of relativity, as it incorrectly states that time passes differently for observers in relative motion. In reality, it is phase shifts in clock oscillation and corresponding wavelength and time distortions. Wavelength is proportional to time (T).

Relativistic effects in time dilation have been verified with biased experiments, as such experiments should have been done on wavelength distortions rather than time dilation. Time, as a concept, does not subject to any experiment on it, unless inviting error. Time is standardised by time standardizing authorities and is not subject to biased experiments.

While these concepts are not distinct, phase shift and wavelength distortions are mutually exclusive, as they are valid scientific interpretations. They are interconnected with time distortion but not with the flawed concept of time dilation.

In recent times, scientists appreciate that these phenomena of time distortions and phase shifts are interconnected and collectively enrich our understanding of the universe, rather than understanding the erroneous time dilation phenomenon. Clocks designed for proper time measurement account for relativistic effects, including time distortion, but not for flawed time dilation.

Universal Gravitational Constant G in Total Mass and Dark Energy Calculations:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

12-06-2024

Abstract:

This analysis examines the consistent use of the universal gravitational constant G in calculations pertaining to both the total gravitating mass (Mɢ = Mᴍ + Mᴅᴇ), encompassing dark matter and baryonic matter, and the effective mass of dark energy (Mᴅᴇ or mᵉᶠᶠ). Through equations derived within the Newtonian gravitational framework, the paper illustrates how the classical universal gravitational constant G is applied to understand gravitational effects within the context of dark energy. By employing the same fundamental constant throughout the analysis, the study ensures conformity with established gravitational laws, reaffirming the role of G in elucidating the dynamics of mass and energy in cosmological structures.

Keywords: Universal Gravitational Constant, Total Mass, Dark Energy, Gravitational Effects, Newtonian Framework,

The analysis of the research on the Coma cluster of galaxies considers the gravitational constant G as the fundamental constant used in both the effective mass of dark energy (Mᴅᴇ) and the total gravitating mass (Mɢ). The known universal gravitational constant G is indeed utilized for calculating the gravitational effects, including those due to dark energy.

Here's how G is applied in the context of the effective mass of dark energy and the total gravitating mass:

1. Effective Gravitating Density of Dark Energy:

The paper uses the equation: ρₑ𝒻𝒻 = ρ + 3P

For dark energy in the ΛCDM model, ρᴅᴇ is the density, and Pᴅᴇ = − ρᴅᴇ, leading to: 

ρᴅᴇₑ𝒻𝒻 = ρᴅᴇ + 3Pᴅᴇ = - 2ρᴅᴇ < 0 

This indicates that the effective density of dark energy is negative, which corresponds to an antigravitational effect.

2. Acceleration Due to Dark Energy:

The gravitational acceleration a(r) at a distance R from the centre of a mass Mᴍ within a uniform dark energy background is given by:

a(R) = - G(Mᴍ/R²) + (4ϖG/3)ρᴅᴇR = aɴ(R) + aᴇ(R)

Here, the second term represents the antigravitational effect of dark energy, and G is the universal gravitational constant. 

aɴ(R) and aᴇ(R) are components of the radial acceleration experienced by a test particle due to gravity and dark energy, respectively.

• Newtonian Gravity Component aɴ(R):

This is the standard Newtonian gravitational acceleration due to a mass Mᴍ at a distance R:

aɴ(R) = - G(Mᴍ/R²)

Here:

• G is the universal gravitational constant.

• Mᴍ is the matter mass causing the gravitational attraction.

• R is the distance from the centre of the mass Mᴍ.

• Dark Energy Component aᴇ(R):

This is the acceleration due to the effect of dark energy, which acts as a repulsive force (antigravity) in this context:

aᴇ(R) = (4ϖG/3)ρᴅᴇR 

Here:

• G is the universal gravitational constant.

• ρᴅᴇ is the density of dark energy.

• R is the distance from the centre of the cluster.

Combined Acceleration

The total radial acceleration a(R) experienced by a test particle at a distance R from the centre of a spherical mass Mᴍ in the presence of dark energy is the sum of these two components:

a(R) = aɴ(R) + aᴇ(R) = - G(Mᴍ/R²) +  (4ϖG/3)ρᴅᴇR

In this equation:

• aɴ(R) represents the attractive gravitational force.

• aᴇ(R) represents the repulsive force due to dark energy.

The balance between these two forces determines the net effect on the particle's motion.

3. Zero-Gravity Radius (Rᴢɢ):

The zero-gravity radius Rᴢɢ, where gravitational and antigravitational forces balance each other, is derived using G:

Rᴢɢ = [Mᴍ/{(8ϖ/3)ρᴅᴇ}]⅓ 

This radius delineates the region where gravity dominates (inside Rᴢɢ) from the region where dark energy dominates (outside Rᴢɢ).

 

4. Dark Energy Mass (Mᴅᴇ):

The effective mass (mᵉᶠᶠ) of dark energy within a radius R is:

Mᴅᴇ(R) = (8ϖ/3)ρᴅᴇR³

 

This shows that Mᴅᴇ depends on ρᴅᴇ and R, but the gravitational effect of this mass is accounted for using G.

The calculations involving Mᴅᴇ and Mɢ are based on the Newtonian gravitational framework where the universal gravitational constant G is consistently used. The paper does not introduce a separate or modified gravitational constant for dark energy; instead, it applies the same G throughout the analysis, ensuring consistency with the established laws of gravity. This approach confirms that the known universal gravitational constant G is used for the effective mass of dark energy (Mᴅᴇ) as well as for other gravitational calculations in the study.

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 & Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781 

#UniversalGravitationalConstant #TotalMass #DarkEnergy #EffectiveMass

Conceptual Analysis of the Antigravitational Force Equation:

The equation: 

- F𝑔 = - G · (m₁ · m₂) / d² 

describes the force of antigravity acting between two masses, m₁ and m₂, separated by a distance d. Here's an analysis of its consequences:

Antigravity Concept: The equation introduces the concept of antigravity, implying a repulsive force between masses rather than an attractive one as described by Newton's law of universal gravitation. This challenges conventional understanding of gravitational forces.

Negative Force: The negative sign indicates that the force is directed away from the masses, opposing their gravitational attraction. This suggests a counterintuitive force acting against gravity.

Inverse Square Law: Similar to Newton's law of gravitation, the force decreases with the square of the distance between the masses (d²). As the distance increases, the force diminishes rapidly.

Magnitude of the Force: The magnitude of the antigravitational force is determined by the gravitational constant (G) and the product of the masses (m₁ and m₂). Larger masses or a smaller distance between them lead to a stronger antigravitational force.

Effects on Gravitational Systems: In systems where both gravity and antigravity are significant, such as clusters of galaxies, this force can influence the dynamics of celestial objects. It could potentially counteract gravitational collapse or affect the overall structure of cosmic systems.

Cosmological Implications: Understanding and quantifying antigravity may have profound implications for cosmology, especially in theories related to dark energy and the expansion of the universe. It could contribute to explanations for phenomena like cosmic acceleration.

Experimental Verification: While theoretical models suggest the existence of antigravity, experimental verification is challenging. Detecting and measuring antigravitational effects would require advanced instrumentation and observational techniques.

In conclusion, the equation represents a departure from traditional gravitational concepts, introducing the idea of antigravity and its potential consequences for our understanding of celestial dynamics and cosmology.

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To Whom It May Concern: 

I multiplied both sides of the equation by -1, intending to make F negative to understand the results... the analysis seems to refer to the results.