Is the Classical Notion of Impulse Based on Quantum Mechanics?

The idea of impulse, i.e. Change in momentum = Integral dt Force appears in Newtonian mechanics. Impulse is considered to be a physical observable, for example it may be linked to the damage done by a particle hitting a target. Impulse, however, only depends on momentum and so two particles with the same momentum, but different masses and velocities may cause the same damage i.e. represent the same physical observable. Momentum in nonrelativistic Newtonian mechanics is m v where m is rest mass and v velocity. Velocity requires a clock in order to measure it, yet two particles with the same momentum and different velocities are considered equivalent in terms of the damage done upon collision with a target i.e the physical impulse. Thus we suggest that time must formally disappear from mv, but this implies that rest mass must behave as t or dt. Furthermore, given Kinetic energy = .5mvv, it must behave as 1/dt. In other words, the reciprocal of kinetic energy behaves as a gradation of time. This is not a standard clock as the gradation is based on a specific kinetic energy and is different for another. In other words, two particles with the same p and different v, have different time gradations. This, however, is a quantum mechanical result. Thus we argue that quantum mechanics may be responsible for the idea of p yielding the same impulse hit for two different v. We further argue that these ideas may be extended to include rest mass with v=0 and to indicate that 1/p is linked to dx, a ruler gradation which is again a quantum mechanical result. Lastly, we argue that these ideas lead to the special relativistic result EE = ppcc + mmcccc and so argue that free particle quantum mechanics and special relativity are closely linked and that classical impulse follows from free particle quantum mechanics