# Have two identical quantum mechanical experiments ever been done?

Have two experiments ever been done such that the set up is identically the same, (when I say identically I mean down to the atomic level). Of course the experiment would have to be very simple. If it has been done do we see differences in the results (as would be expected with the probabilistic nature of quantum mechanics)? If not, what are the limitations preventing us from doing such an experiment?

• What do you mean "down to the atomic level"? Many QM experiments have been repeated over and over again, just think of all the teachers that show the double slit to their student! – ACuriousMind May 25 '15 at 17:46
• @ACuriousMind I mean that if you looked at the experimental set up down to an the size of atoms, they would be indistinguishable. – Quantum spaghettification May 25 '15 at 18:04
• That would trivially be achieved by just running the measurement apparatus once today and again tomorrow, wouldn't it? – ACuriousMind May 25 '15 at 18:14
• @ACuriousMind As long as you can make sure no 'atoms move' and that for example the same atom decays etc – Quantum spaghettification May 25 '15 at 18:19
• @Joseph your last comment makes no sense. At the atomic level one is in the Heisenberg Uncertainty Principle range and no such controls can even be imagined. – anna v May 27 '15 at 14:07

As for the probabilistic aspect, this is not really the right way to look at "an experiment." Suppose we have have an experiment that's the quantum equivalent of a coin-flip. Maybe we excite an atom in such a way that it can emit either $A$ light or $B$ light with a 50% probability. (If you're more familiar with quantum mechanics, a better example is a Stern-Gerlach experiment.) Ok, so we load the atom into a trap, hit it with a laser, and wait to see whether the $A$ or the $B$ detector clicks. That's the experiment.