I have recently read that momentum transfer is not instantaneously. This is obvious enough considering a moving billiards ball hitting into a stationary one. They do not instantly go to their new speeds. There is some acceleration time. What I wish to know is what governs how long this accelerating time is? How long passes before the momentum is fully transferred? Also do the same rules apply to momentum transfer for a photon?
It depends on the nature of your objects. In case of elastic balls one has to solve problems of elasticity or can estimate roughly as the time necessary for elastic wave to travel through ball, maybe twice. In case of atoms and electrons, protons etc. there is never such collision as in case of macroscopic objects. The accelerating process is given by equations of particle motion in electric field - well known "two body" problem of mechanics. The momentum change is gradual and for Coulomb potential the time of total momentum transfer - infinite.
It depends on the nature of your objects. In case of elastic balls one has to solve problems of elasticity or can estimate roughly as the time necessary for elastic wave to travel through ball, maybe twice. In case of atoms and electrons, protons etc. there is never such collision as in case of macroscopic objects. The accelerating process is given by equations of particle motion in electric field - well known "two body" problem of mechanics. The momentum change is gradual and for Coulomb potential the time of total momentum transfer - infinite.
I believe that first estimation for the momentum transfer time could be derived from simplest physical considerations, on the base of dimensional analysis, for instance. Time of momentum transfer will depend on the type of the forces acting during the interaction. Infinite interaction time - generally has no physical sense. In most cases one can find characteristic time that determines the process.
There is no characteristic length in Coulomb (or gravitational) potential. One can artificially chose 90% or 99% limit of momentum transfer and calculate corresponding time for given velocity and collision parameter. In reality the length is limited by surroundings -- in plasma by Debye length, in gas or plasma by mean free path. The mean free path is usually considered as a distance between instantaneous acts of collisions. In fact it is distance at which the momentum transfer occurs with given scatterer (the last one). Then the next scatterer enters the play etc.
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