Soumendra
Nath Thakur
ORCiD: 0000-0003-1871-7803
Abstract:
This study serves as a supplementary resource for researchers investigating length deformation in classical and relativistic mechanics. It complements existing studies such as the 'Comparative Analysis of Length Deformation in Classical and Relativistic Mechanics' series, 'Dynamics between Classical Mechanics and Relativistic Insights', and 'Advancing Understanding of External Forces and Frequency Distortion: Part -1.'
The focus of this resource is on the intricate dynamics of mass and effective mass, exploring fundamental concepts like matter mass and gravitating mass. The relationship between effective mass and forms of energy is examined in detail, elucidating how effective mass accounts for resistance to acceleration or changes in velocity under gravitational forces, akin to the gravitational potential energy of inertial mass.
Through a detailed analysis and illustrative examples, including the study 'Dark Energy and the Structure of the Coma Cluster of Galaxies,' the interplay between matter and dark energy is deciphered. This offers profound insights into the complex dynamics of the universe, shedding light on the interaction between matter and dark energy.
This resource serves as a supplementary guide for researchers investigating length
deformation in classical and relativistic mechanics. It complements studies
such as the 'Comparative Analysis of Length Deformation in Classical and
Relativistic Mechanics' series,[₁,¹, ₂,²] 'Dynamics between Classical Mechanics and Relativistic
Insights'[₃,³], and 'Advancing Understanding of External Forces and
Frequency Distortion: Part -1.'[₄,⁴]
Delve into nuanced discussions on mass and effective mass, covering fundamental
concepts like matter mass and gravitating mass. Explore the intricate
relationship between effective mass and forms of energy, understanding how it
accounts for resistance to acceleration or changes in velocity under
gravitational forces, akin to the gravitational potential energy of inertial
mass. Through examples like the study 'Dark Energy and the Structure of the
Coma Cluster of Galaxies,'[₅,⁵]
witness how this resource deciphers the interplay between matter and dark
energy, offering profound insights into their intricate dynamics.
Keywords: Matter Mass, Gravitating Mass, Effective mass, Dark energy.
The Concepts of Mass:
1. Matter Mass (Mᴍ):
The matter mass (Mᴍ) is a measure of the amount of matter in a substance or object. Anything that has volume and mass is classified as matter. Although mass itself cannot be seen, it is quantifiable and can be measured. The basic SI unit for mass is the kilogram (kg). The only entities that are not matter are forms of energy.
Mass vs. Weight: Mass is often confused with weight, but they measure different things. Mass measures the amount of matter in an object, while weight measures the force of gravity acting on that object. The force of gravity on an object depends on its mass and the strength of gravity. If the strength of gravity is held constant (as it is across the Earth), an object’s mass is directly proportional to its weight, meaning greater mass corresponds to greater weight.
Volume measures the amount of space that a substance or object occupies. The basic SI unit for volume is the cubic meter (m³), but smaller volumes may be measured in cubic centimeters (cm³), and liquids may be measured in liters (L) or milliliters (mL). The method used to measure the volume of matter depends on its state.
2. Gravitating Mass (Mɢ):
The gravitating mass (Mɢ) is the mass of an object as measured in a gravitational field. This requires a gravitational field, a scale, and various known masses.
Inertial Mass vs. Gravitational Mass: Inertial mass and gravitational mass of an object are identical in value but differ in their measurement methods. Inertial mass is measured by assessing an object's resistance to changes in velocity, while gravitational mass describes the force on an object within a gravitational field. Inertial mass is derived from the concept of inertia—the tendency of objects to remain motionless or in uniform motion unless acted upon by a force. Gravitational mass is measured using a scale.
Since the motion of an object on a spring involves constant changes in velocity, and the behavior of the spring system is related to the mass on the spring, inertial mass is often measured by attaching a mass to a spring. This involves using a spring with a known spring constant (k), which describes the 'stiffness' of the spring.
3. Effective Mass (mᵉᶠᶠ):
Energy, while not matter, is equivalent to mass. The concept of effective mass (mᵉᶠᶠ) refers to the mass equivalent of the gravitational effect of forms of energy.
Effective mass accounts for the resistance to acceleration or changes in velocity of a particle when responding to a gravitational force. This is similar to how the gravitational potential energy of any inertial mass contributes to resistance to acceleration or changes in velocity.
In this context, the effective mass represents the mass equivalent of the gravitational effects of forms of energy, accounting for resistance to acceleration or changes in velocity. Thus, effective mass is the representation of the mass equivalent of energy's resistance to acceleration under the influence of gravitational force.
Therefore, the effective mass is the mass equivalent of the gravitational effect of forms of energy, representing their resistance to acceleration or changes in velocity when responding to specific forces. This concept is similar to the gravitational potential energy of any inertial mass, which also accounts for resistance to acceleration or changes in velocity.
Example:
The study "Dark Energy and the Structure of the Coma Cluster of Galaxies" by A. D. Chernin et al. explores the mass distribution within the Coma cluster, introducing the concept of gravitating mass (Mɢ), which represents the cluster's total mass, and effective mass (Mᴅᴇ or mᵉᶠᶠ), indicating the mass equivalent of dark energy's gravitational effect. The effective mass is defined as the difference between the gravitating mass and the matter mass (Mᴅᴇ = Mɢ − Mᴍ). This equation highlights the contribution of dark energy within a specific radius. By distinguishing between matter mass (Mᴍ), dark-energy effective mass (Mᴅᴇ <0), and gravitating mass (Mɢ = Mᴍ + Mᴅᴇ), the study provides a detailed understanding of the interaction between matter and dark energy in the cluster's structure and dynamics.
References:
1. Thakur, S.
N. Comparative Analysis of Length Deformation in Classical and Relativistic
Mechanics. Preprints.org. https://doi.org/10.20944/preprints202405.1271.v1
2. Thakur, S.
N. Comparative Analysis of Length Deformation in Classical and Relativistic
Mechanics: Part-2. Preprints.org. https://doi.org/10.20944/preprints202405.1332.v1
3. Thakur, S.
N. Dynamics between Classical Mechanics and Relativistic Insights:
ResearchGate. https://doi.org/10.13140/RG.2.2.21005.96481/1
4. Thakur, S.
N. Advancing Understanding of External Forces and Frequency Distortion: Part
-1. ResearchGate. https://doi.org/10.13140/RG.2.2.35236.28809
5. 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
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