The second boundary condition is imposed so that the metric at the boundary is continuous with the unique static spherically symmetric solution to the vacuum field equations, the Schwarzschild metric:
22.
They further suggested that, as a particle translates, this vibrational motion interacts selectively with waves in the ambient vacuum field, a resonant interaction that amplifies an electromagnetic pilot wave.
23.
To obtain the vacuum field equations, we must vary the gravitational term in the Lagrangian with respect to the metric g _ { a b }; this gives the second field equation above.
24.
However, when we do this and solve the Heisenberg equation for a field operator, we must include the vacuum field, which is the homogeneous part of the solution for the field operator.
25.
Photon-photon interaction can occur only through interaction with the vacuum state of some other field, for example through the Dirac electron-positron vacuum field; this is associated with the concept of vacuum polarization.
26.
This has the result of changing the vacuum field equation from the Laplace equation to the wave equation, which means that any " news " concerning redistribution of matter in one location is transmitted at the speed of light to other locations.
27.
The zero-point energy cannot be eliminated by dropping its energy from the Hamiltonian : When we do this and solve the Heisenberg equation for a field operator, we must include the vacuum field, which is the homogeneous part of the solution for the field operator.
28.
The spectral density of the vacuum field is fixed by the form of the radiation reaction field, or vice versa : because the radiation reaction field varies with the third derivative of, the spectral energy density of the vacuum field must be proportional to the third power of in order for to hold.
29.
The spectral density of the vacuum field is fixed by the form of the radiation reaction field, or vice versa : because the radiation reaction field varies with the third derivative of, the spectral energy density of the vacuum field must be proportional to the third power of in order for to hold.
30.
Vacuum field perturbations are simulated by fluid field perturbations and the aerodynamic resistance of viscous drag exerted on the interior of the vehicle is compared to the Lorentz force exerted by the zero-point field ( a Casimir-like force is exerted on the exterior by unbalanced zero-point radiation pressures ).
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