On 21 Apr., 16:56, netzweltler <reinhard_fisc...@arcor.de> wrote: > On 21 Apr., 16:03, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 21 Apr., 12:22, netzweltler <reinhard_fisc...@arcor.de> wrote: > > > > On 21 Apr., 11:07, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 21 Apr., 10:02, netzweltler <reinhard_fisc...@arcor.de> wrote: > > > > > > On 20 Apr., 19:03, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > All atoms of the accessible universe and all positions they can take > > > > > > belong to a finite set. > > > > > > How do we prove, that the number of possible positions an atom can > > > > > take along a line of 1 cm is finite? > > > > > By accepting quantum mechanics and excluding theology (these > > > > assumptions taken as axioms for those who believe (as an axiom) to > > > > need axioms) a proof is given here:http://arxiv.org/ftp/arxiv/papers/0709/0709.4102.pdf > > > > pages 2-3. > > > > > Regards, WM > > > > What about a position between two quanta? Should there be no decimal > > > fraction for a position between two adjacent quanta along this line of > > > 1 cm?- > > > Quantum theory tells us, contrary to Einsteins's false beliefs, that > > unmeasurable events do not exist. The electron or photon does not > > simultaneously have fixed position and momentum (that would contradict > > some results of interference experiments). > > 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.