Invariant energy – wikiversity electricity generation definition

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If we take into account the definition of 4-velocity: u μ = d x μ d τ {\displaystyle ~u^{\mu }={\frac {dx^{\mu }}{d\tau }}} , where d x μ {\displaystyle ~dx^{\mu }} is 4-displacement vector, d τ {\displaystyle ~d\tau } is the differential of the proper time; and the definition of the spacetime interval: d s = g μ ν d x μ d x ν = c d τ {\displaystyle ~ds={\sqrt {g_{\mu \nu }dx^{\mu }dx^{\nu }}}=cd\tau } , then again we obtain the equality: E 0 = M c 2 {\displaystyle electricity of the heart ~E_{0}=Mc^{2}} .

In elementary particle physics the interaction of several particles, their coalescence and decay with formation of new particles are often considered. Conservation of the sum of 4-momenta of free particles before and after the reaction leads to the conservation laws of energy and momentum of the system of particles under consideration. The invariant energy E 0 c {\displaystyle ~E_{0c}} of the system electricity in the body symptoms of particles is calculated as their total relativistic energy in the reference frame in which the center of momentum of the particle system is stationary. In this case E 0 c {\displaystyle ~E_{0c}} can differ from the sum of invariant energies of the particles of the system, since the contribution into E 0 c {\displaystyle ~E_{0c}} is made not only by the rest energies of the particles, but also by the kinetic energies of the particles and their potential energy. [2] If we observe the particles before or after the interaction at large distances from each other, when their mutual potential energy can be neglected, the invariant energy of the system is defined as:

In determining the invariant energy of a massive body in general gas upper stomach relativity (GR) there is a problem with the contribution of the gravitational field energy, [3] since the stress-energy tensor of gravitational field is not clearly defined, and stress-energy-momentum pseudotensor is used instead. In case of asymptotically flat spacetime at infinity for the estimation of the invariant energy the ADM formalism for the mass-energy of the body can be applied. [4] For the stationary spacetime metric the Komar mass and energy are determined. [5] There are other approaches basic electricity quizlet to determination of the mass-energy, such as Bondi energy, [6] and Hawking energy.

where the mass m b {\displaystyle ~m_{b}} and charge q b {\displaystyle ~q_{b}} of body are obtained by integrating the corresponding density by volume, E k {\displaystyle ~E_{k}} is the energy of motion of particles inside the gas 76 station body, G {\displaystyle ~G} is the gravitational constant, a {\displaystyle ~a} is the radius of the body, ε 0 {\displaystyle ~\varepsilon _{0}} is the electric constant, E p {\displaystyle ~E_{p}} is the pressure energy.

In covariant theory of gravitation (CTG) in the calculation of the invariant energy the energy partition into 2 main parts is used – for the components of the energy fields themselves and for components associated with the energy of the particles in these fields. Calculation shows that the sum of the components of the energy of acceleration field, pressure grade 9 electricity review field, gravitational and electromagnetic fields, for the spherical shape of the body is zero. [8]

In this case the inertial mass system M {\displaystyle ~M} should be equal to the total mass of particles m ′ {\displaystyle ~m’} , the mass m b {\displaystyle ~m_{b}} equals the gravitational mass m g {\displaystyle ~m_{g}} and excess m b {\displaystyle ~m_{b}} over M {\displaystyle ~M} is due to the fact that particles move inside the body and are under pressure electricity units of measurement in the gravitational and electromagnetic fields.

For the case of a relativistic uniform system, the invariant energy can be expressed as: [10] [11] E 0 = M c 2 ≈ m b c 2 − 1 10 γ c ( 7 − 27 2 14 ) ( G m b 2 a − q b 2 4 π ε 0 a ) . {\displaystyle ~E_{0}=Mc^{2}\approx m_{b}c^{2}-{\frac {1}{10\gamma _{c}}}\left(7-{\frac {27}{2{\sqrt {14}}}}\right)\left({\frac {Gm_{b}^{2}}{a}}-{\frac {q_{b}^{2}}{4\pi \varepsilon _{0}a}}\right).}

Here the gauge mass m ′ {\displaystyle ~m’} is related to the cosmological constant and represents the mass-energy of the matter’s particles in the four-potentials of the system’s fields; the inertial mass M {\displaystyle ~M} ; the auxiliary mass m {\displaystyle ~m} is equal to the product of the particles’ mass density by the volume of the system; the mass m b {\displaystyle ~m_{b}} is the sum of the invariant masses (rest masses) of the system’s particles, which is equal in value to the gravitational mass m g {\displaystyle gas vs electric water heater cost per year ~m_{g}} .

These formulas remain valid at the atomic level, with the difference that the usual gravity replaced by strong gravitation. In the covariant theory of gravitation based on the principle of least action is shown that the gravitational mass m g {\displaystyle ~m_{g}} of the system increases due to the contribution of mass-energy of the gravitational field, and decreases due to the contribution u gas station near me of the electromagnetic mass-energy. This is the consequence of the fact that in LITG and in CTG the gravitational stress-energy tensor is accurately determined, which is one of the sources for the determining the metric, energy and the equations of motion of matter and field. The acceleration stress-energy tensor, dissipation stress-energy tensor and pressure stress-energy tensor are also identified in covariant form.

Vector fields such as the gravitational and electromagnetic fields, the acceleration field, the pressure field, the dissipation field, the fields of strong and weak interactions are components of general field. This leads to the fact that the invariant energy of the gas tax in texas system of particles and fields can be calculated as the volumetric integral in the center-of-momentum frame: [12] E = ∫ ( s 0 J 0 + c 2 16 π ϖ s μ ν s μ ν ) − g d x 1 d x 2 d x 3 , {\displaystyle ~E=\int {(s_{0}J^{0}+{\frac {c^{2}}{16\pi \varpi }}s_{\mu \nu }s^{\mu \nu }){\sqrt {-g}}dx^{1}dx^{2}dx^{3}},}