Relativity mass
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Relativity and Mass: Key Insights from Recent Research
Relativistic Mass and Observer Dependence
In the realm of relativity, mass is not an absolute quantity but depends on the observer's frame of reference. This concept is central to understanding relativistic mass, which varies with the velocity of the observer relative to the object in question. The Lorentz transformation plays a crucial role in defining this relativistic mass, as it relates the rest mass of a particle to its observed mass when in motion2. This transformation is mathematically expressed as ( m_r(v) = \gamma(v) m_0 ), where ( \gamma(v) ) is the Lorentz factor, ( m_0 ) is the rest mass, and ( v ) is the velocity of the particle relative to the observer4.
Mass in General Relativity
In general relativity, the concept of mass becomes even more complex. The Denisov-Solov'ov example illustrates that inertial mass is not well-defined within this framework due to the improper application of the Stokes theorem3. Additionally, the definition of mass in general relativity is influenced by the order of asymptotic flatness, which affects how mass is perceived at different scales and distances3.
Equivalence of Inertial and Gravitational Mass
The principle of equivalence, a cornerstone of general relativity, posits that inertial mass and gravitational mass are equivalent. This principle has been experimentally confirmed with high precision using torsion balance measurements, which show no significant difference between the ratios of gravitational to inertial mass for different materials5. This experimental validation supports Einstein's foundational assumption in general relativity5.
Mass and Energy in General Relativity
Mass in general relativity is intricately linked to energy. The total energy in a system, including contributions from gravitational binding energy, is considered the source of gravity. This perspective aligns with the modern understanding that rest-mass energy is likely the gravitational binding energy of a particle within the universe's gravitational horizon6. This holistic view integrates various interpretations of mass, from inertia to gravitational coupling, under the umbrella of total energy6.
Quantum Entanglement and Gravitational Interaction
Recent studies have explored the quantum gravitational entanglement of masses, revealing that non-local gravitational interactions can influence the entanglement properties of particles. For instance, the gravitational energy shift, which is operator-valued in linearized general relativity, affects the entanglement of test masses treated as harmonic oscillators or in quantum spatial superposition7. These findings highlight the interplay between quantum mechanics and general relativity in understanding mass and gravitational interactions7.
Gauss' Theorem and Mass in General Relativity
Gauss' theorem, traditionally applied to Newtonian gravity, has been extended to general relativity. In this extended form, the concept of "gravitating mass" is replaced by the energy-tensor, which can include contributions from fields such as electrostatic fields, not just material masses8. This extension underscores the broader applicability of Gauss' theorem in describing gravitational phenomena in general relativity8.
Conclusion
The concept of mass in relativity is multifaceted, varying with the observer's frame of reference and integrating deeply with energy in general relativity. Experimental validations of the equivalence principle and extensions of classical theorems to relativistic contexts further enrich our understanding. As research continues to bridge quantum mechanics and general relativity, our grasp of mass and its implications in the universe will undoubtedly evolve.
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UNIFORMLY ACCELERATING CHARGED MASS IN GENERAL RELATIVITY.
The solution of the Einstein-Maxwell equations for a uniformly accelerating charged mass is a direct generalization of the Reissner-Nordstrom solution and the Born solution in classical electrodynamics.
Highly CitedMass and energy in General Relativity
The inertial mass in General Relativity is not well defined due to a wrong application of the Stokes theorem and the role of asymptotically flatness in the definition of mass.
Definitions of mass in special relativity
The TW approach to mass definition in special relativity has a problem with the definition of momentum and energy, as it does not include the relativistic mass concept.
The equivalence of inertial and passive gravitational mass
The principle of equivalence between inertial and passive gravitational mass remains valid for all materials, as demonstrated by the most sensitive torsion balance measurements.
Highly CitedInertia, gravity and the meaning of mass
The concept of mass has evolved over time, and recent developments in cosmology show that rest-mass energy is likely the gravitational binding energy of a particle in contact with the universe within our gravitational horizon.
Quantum entanglement of masses with nonlocal gravitational interaction
Quantum gravitational entanglement of masses can be induced by non-local gravitational interaction, leading to a decrease in concurrence and von Neumann entropy.
On Gauss' theorem and the concept of mass in general relativity
The extended Gauss' theorem in general relativity theory enables us to express the gravitational theorem of 2 in a way identical to the original Newtonian theorem, while also allowing for the electrostatical form of Gauss' theorem to be extended to General
Highly CitedOn Slowly Rotating Homogeneous Masses in General Relativity
Slowly rotating homogeneous masses in general relativity exhibit a maximum ellipticity at R/R s 2.4, with a natural limit at 9/8 times the Schwarzschild radius.
Highly CitedNew General Relativity
New general relativity, with c/sub 1/ = 0 = c/sub 2/, demonstrates that a static, spherically symmetric gravitational field is given by the Schwarzschild metric, and agrees with all current experiments.
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