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.

Gravitational and Antigravitational Influences on the Speed of Light:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

09-06-2024

The speed of light, denoted as c, is determined by the product of its frequency (f) and wavelength (λ), as expressed by the equation c = f·λ. This relationship indicates that when there are no external forces acting upon a wave or photon, both its frequency and wavelength remain constant. However, when a photon is emitted from a gravitationally bound body, it is subjected to the gravitational force, represented by F𝑔 = G · (m₁ · m₂) / d², where G is the gravitational constant, m₁ and m₂ are the masses of the bodies involved, and d is the distance between them.

The gravitational force exerted influences the wavelength, causing it to undergo redshift. Despite this shift, the speed of light remains constant. This constancy is maintained because the frequency of the wave or photon also changes in accordance with the inverse relationship f ∝ 1/λ. As the wavelength increases due to gravitational effects, the frequency decreases proportionally, ensuring c remains unchanged.

The decrease in frequency results in a reduction of the wave's energy (E), as described by the equation E = hf, where h is Planck's constant. The gravitational force continues to affect the wave or photon until its influence becomes negligible, described by the condition F𝑔 = G · (m₁ · m₂) / d².

Upon surpassing the gravitational influence, the wave or photon encounters a negative gravitational force, referred to as antigravity, expressed as - F𝑔 = - G · (m₁ · m₂) / d². In such instances, the usual distance travelled (>c) when the wave or photon speed equals c, f·λ = c, is surpassed. Consequently, the wave or photon is compelled to adhere to f·λ > c, leading to a permanent increase in wavelength. As a result, frequency and energy decrease in correspondence with the equation E = hf, even as the wave or photon maintains a speed following c = f·λ, even when it surpasses c over distance. Thus, gravitational influences play a crucial role in determining and confirming the speed of light.

#gravitationalredshift, #cosmicredshift, #darkenergy, #cosmicexpansion, #photonenergy, #frequencywavelengthrelationship, #antigravity, #Zerogravityradius

Gravitational and Dark Energy Influences on Light:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

09-06-2024

Abstract:

The speed of light (c) is governed by the equation c=f⋅λ, where frequency (f) and wavelength (λ) are inversely proportional. This relationship ensures that in the absence of external forces, both frequency and wavelength remain constant. However, photons emitted by gravitationally bound bodies experience a gravitational force, described by Fg = G⋅(m₁⋅m₂)/d², influencing their wavelength and causing redshift. Despite this, the speed of light (c) remains unchanged due to the compensatory relationship between frequency and wavelength. As gravitational redshift reduces the frequency, the energy of the photon decreases according to E=hf. Beyond the gravitational influence, photons encounter the effects of dark energy, which exhibits antigravitational properties and becomes significant in cosmic expansion. This study highlights that while light travels at a constant speed in a vacuum, the increasing distance due to cosmic expansion can be perceived as (c+Δd)>c, though the intrinsic speed of light remains c. These findings underscore the importance of gravitational and dark energy influences on light while affirming the constancy of the speed of light in a vacuum.

Keywords: Gravitational redshift, Cosmic redshift, Dark energy, Cosmic expansion, Photon energy, Frequency-wavelength relationship, Antigravity, Zero-gravity radius,

The speed of light (c) is given by the equation c=f⋅λ, where frequency (f) is inversely proportional to wavelength (λ), i.e., f∝1/λ. This means that in the absence of any external forces acting on a wave or photon, both the frequency and wavelength would remain unchanged. However, the source emitting a photon is a gravitationally bound body. Therefore, a gravitational force acts on the wave or photon from the moment of its emission until it exits the gravitational influence of its source. This force is expressed as:

Fg = G⋅(m₁⋅m₂)/d²

The gravitational force (Fg) influences the wavelength (λ), causing redshift, although c remains constant. This is possible because the frequency (f) of the wave or photon must also change due to their relationship f∝1/λ. As the wavelength increases due to the gravitational force (Fg), the frequency (f) correspondingly decreases, ensuring that c remains constant. A reduction in f leads to a reduction in the energy (E) of the wave, as described by E=hf. Consequently, the energy of the wave or photon decreases due to the gravitational force (F_g) until this force becomes negligible, according to the relationship Fg = G⋅(m₁⋅m₂)/d².

When the wave or photon moves beyond the gravitational influence, it no longer experiences redshift or blueshift due to gravity. Beyond gravitational influence, dark energy, which exhibits antigravitational properties, can become significant. This is discussed in the study "Dark energy and the structure of the Coma cluster of galaxies" by Chernin et al. (2013), where dark energy's repulsive effect influences the structure of the Coma cluster. The effective mass of dark energy is considered negative due to its repulsive nature, impacting the cluster's dynamics.

In the context of cosmic expansion, this means that as the wave or photon travels through regions where dark energy dominates, the increasing distance due to cosmic expansion affects the observed wavelength (λ) and frequency (f). While light always travels at the speed c in a vacuum, the increasing distance (c+Δd) due to cosmic expansion can be interpreted as (c+Δd)>c. However, the intrinsic speed of light remains c.

Thus, gravitational influences and cosmic expansion affect the frequency and wavelength of light but do not alter the constancy of the speed of light (c) in a vacuum.

References:

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

#gravitationalredshift, #cosmicredshift, #darkenergy, #cosmicexpansion, #photonenergy, #frequencywavelengthrelationship, #antigravity, #Zerogravityradius