A spherical shock front is a solution of a second order partial differential equation, such as the well known wave equation. The shock front is not a wave and it is not a wave package. During travel the shape of the front is constant and its amplitude diminishes as 1/r with distance r from the trigger location. The pulse response integrates over time into the Green's function of the carrier field. This is a solution of the Poisson equation. It has shape 1/r. It contains some volume. This volume is inserted into the carrier field. This locally deforms the field. Subsequently, this volume spreads over the full field as is shown by the dynamics if the spherical pulse response. Thus, the local deformation quickly fades away.
The deformation of the carrier field means that temporary the spherical pulse response owns a small amount of mass, but this mass quickly dilutes in the expansion of the carrier field.
To my knowledge the spherical pulse response is the only field excitation that locally and temporarily deforms this field.
The stochastic processes that generate the temporary locations of elementary particles use this mechanism to provide that particle with persistent mass by recurrently regenerating the hopping path of the particle. .
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