 2360 Shisheng Wang
 A unified dynamic equation of the classical field in local manifold
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Sep 28, 23

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Abstract. The fluid dynamics, gravitational field dynamics, and electromagnetic field dynamics can be expressed as a unified field equation in a local inertial frame by D_t p ⃗=∇L, where p ⃗ is the momentum vector, and L is the Lagrangian s density. In a timefreezing configuration (static state), the stored energy density and the mass density in the instantaneous configuration have the relation of p=ρc^2. It can be positive (potential energy) or negative (binding energy), depending on the zero potential energy definition point in the field. Its sign only affects the chirality. Given a slight motion in a local inertial frame, the momentum vector field and potential energy field are combined into a single physical field a 4momentum vector field. In general, for a manyparticle system, the interactions between particles obey the weak law of action and reaction. The action and interaction forces can be decomposed into two components: one is along the jointing line to consider the linear momentum, and another one is perpendicular to the jointing line to consider the rotational motion. It is suggested that the fluid dynamics equations should include an extra term, a Coriolislike force term, to consider the spin (or rotational) effect (because of the vorticity field). Electromagnetic fields have no rest frame; they have an intrinsic 4momentum vector relative to a rest observer. With the 4momentum vector the Maxwell equations can be deduced. In a vacuum , each of the electric field and magnetic field contribute half to the total energy. It implies that the linear and rotational kinetic energy equals each other. The Gauss law thinks of an electrical dipole as a vacuum space; this implies that photon gas is composed of a mixture of electrical dipoles. Their trajectories will be helical or spiral, as is shown by the circular polarized Electromagnetic waves.
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