ok, but let's think this through for a minute.

the difference is i*h-bar. h-bar is h/2*pi.

h is considered to be the smallest possible unit of measurement, and then you're dividing the smallest possible unit of measurement by 2*pi to make it that much smaller. you're then pulling this out in the direction of i.

so, the difference is

1) in the direction of the imaginary plane.

2) a factor of 2*pi smaller than the smallest thing that can be measured.

i'm not arguing with the  math as it exists, it's just that this is so small as to be indiscernible from error, which is what the physics really says - you're disturbing the system by measuring it.

and, i will hear an army of math-physics nerds yell at me "no. it's a proof. can't you see?"

a proof by a factor of h/2*pi in the imaginary plane. right. and, you call that "observable". what a farce! it would be a talented lab technician indeed that could reduce error to hbar in the imaginary direction. you'd give that technician a nobel prize....

rather, i need to ask the question - how fast is space expanding, anyways? surely fast enough that you could never get it right, to a plank length. and, what is the proper correction for the curvature of space, given that we're modeling everything in euclidean vector spaces and we know that is totally wrong?

that's something we can calculate, right?

we know that px - xp, if calculated in a euclidean vector space, should have a correction term, because the space that the particle is moving in is actually curved. that euclidean calculation should be wrong. so, what is the error term, there?

and, without bringing in string theory, what is this modulation in the i direction anyways? if space is expanding constantly in every direction, just how close can we get those measurements without having the rug pulled out from underneath us, as we're doing it? a plank length? probably not much more than it, anyways.

i know that somebody will tell me i'm grasping at straws, but we should at least have the good sense not to be building modern physics on euclidean space. we know that's a bad model. we know that's going to created warped results.