On 21 Apr., 21:32, netzweltler <reinhard_fisc...@arcor.de> wrote: > On 21 Apr., 18:06, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 21 Apr., 16:56, netzweltler <reinhard_fisc...@arcor.de> wrote: > > > > If non-measurable distances don't exist, don't we face another > > > problem? Let's say, d is the smallest distance that can be measured. > > > Distances below d don't exist. So, d/2 is a non-existing distance. Is > > > it still valid, that d/2 + d/2 = d then? I mean, how can distance d > > > exist, if it is composed of two non-existing distances d/2?- > > > The old problem of Aristotle: How can a resting body come to move? > > There must be a point of time where rest and movement are > > simultaneously realized. But that is impossible. > > > Concerning mathematics, there is d/2 even for d = 10^-1000000 fm. > > Thats facilitated by invention of the system of fractions. But you had > > asked for real atoms. > > Yes. I am still asking for _real_ distances. > > If there is a d/2 for any d, how can we say, that the number of > positions of an atom is finite?
In reality there is not a d/2 for every d. The shortest possible wave cannot be shortened and cannot be used to find a shorter d than its wavelength or a finite fraction of it. Further, if the shortest possible wave is created, there are no atoms marking a distance any longer and no men to measure it, because all energy has been used to create the wave.