In Part I we noted that in quantum mechanics, and even in the case of special relativity, there is an arbitrariness associated with x and t. For example, momentum in one dimension is exactly 0. One cannot arbitrarily shift it. If x=0, however, this is arbitrary, it may be shifted. We argued that this arbitrariness and the independence of x and t in a rest frame mo, x=0, t=to should carry over into the results seen in a moving frame, but in that case x'/t'=v because a Lorentz transformation

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... (x=0,t=0) to (x'=0, t'=0). Thus it appears that the arbitrariness of x,t and their independence have been broken, but we argue that a special Lorentz invariant -Et+px restores it by creating a time period hbar/E and wavelength hbar/p. In other words, a mathematical point is an abstraction representing a wavelength region defined by p through a complex probability exp(ipx) i.e. the wavefunction (and a similar exp(-iEt for time). In this note, we focus on these points in further detail. A point x is associated with p or -p in one dimension, but a distribution, say cos(px), combines a fixed p with probabilities and gives the impression of positive and negative momentum values when the slope is positive or negative. Thus cos(px) by itself shows no overall translational motion, but contains regions of positive or negative momentum i.e. zero point motion. One must superimpose on this zero point motion (which exists for all energies) actual "translation" to the right or left. Given that positive and negative p's already exist in one dimension which have nothing to do with translation, one is forced to move into a second dimension to create the translational motion which is associated with a probability such that each x point has the same value. This then leads to exp(ipx). Next we consider a bound state situation. In the case of exp(ipx), cos(px) and sin(px) are linked to the positive/negative zero point type energy which has nothing to do with translation, while p has everything to d [...]