Quantum and Classical Mechanics and Two Delivery Schemes for Force

In this note we argue there exist two force delivery schemes which are already well-known in classical mechanics namely: F(x)dx and F(t)dt. The former is associated with work and kinetic energy, is deterministic (yields x(t)) and requires information about velocity (or rest mass). It deals with F(x) where F=Force. The second is associated with an impulse which changes momentum. In this case, one does not need to know the rest mass or velocity. For example, a particle with momentum p (this allows for many mo,v pairs with the same p) strikes a surface and is reflected back with -p. It is also associated with probability as such a scenario exists for light reflecting and refracting from a surface. One does not know a priori the probabilities for these two phenomena so the problem is probabilistic. Classical mechanics primarily deals with the F(x) force delivery scheme, e.g. solving a differential equation(s) which arise directly from dp/dt = F(x) or using Lagrange’s or Hamilton’s formalism. Ultimately one obtains the deterministic result x(t). Although the notion of an impulse is well-known in Newtonian mechanics, it does not seem to be used much in calculations because an explicit form of F(t) is usually not known i.e. the force acts in a very tiny dx region in a very short period of time. As noted above, both schemes i.e. both deterministic and probabilistic situations appear in the macroscopic classical world, yet for some reason it is suggested that Newtonian mechanics is only deterministic. Newton considered a photon to be a particle with momentum p. A single photon reaching a surface with a different index of refraction has a certain probability to reflect and another to refract. This is a probabilistic, not deterministic, scenario governed by an impulse delivery. The probabilistic problem of light reflecting and refracting in a macroscopic situation may be solved by using continuity of the periodic electric field and its derivative from Maxwell’s solution for a photon from his electromagnetic equations. We have suggested in previous notes, however, that no knowledge of Maxwell’s result is needed. A steady state reflection/refraction problem removes time (unlike the x(t) deterministic picture), but seems to require some kind of balance on the right and left hand sides of the medium. Furthermore two equations are needed to solve for the two unknowns (i.e. reflection and refraction probabilities). Intensity/flux does not balance because the incident and reflected rays have positive flux. For n1