In the Schrödinger's cat experiment 'there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays'. The rest of the experiment magnifies this into a macroscopic superposition, but I want to know more about the claim that the radioactive decay produces a superposition.

Firstly, has this been experimentally tested? Something along the lines of accelerating radioactive ions so there is a chance that they will decay while in flight (and so change trajectory), and then combining the decayed and undecayed parts to look for interference.

Secondly, the tiny bit of radioactive substance will still contain large numbers of atoms. Won't this cause problems? If the atoms were in a Bose-Einstein condensate, then I would expect that there could be a superposition of 'one (unspecified) atom decayed' and 'no atoms decayed', but they're not, so a specific atom will decay. Won't that mess things up?

• Don't know if the experiment you describe has been performed, but for the second part of your question: there's nothing to say you can't get a superposition of the form $\left|\text{no atoms decayed}\right> + \left|\text{atom #36246002 decayed}\right>$! If the nuclear recoil is large enough you'll rapidly get decoherence however, and in practice you won't be able to do an interference experiment. – Michael Brown Jan 9 '13 at 10:05

The existence of superpositions of the type $$|\psi\rangle = \exp(-\Gamma t/2)|{\rm undecayed}\rangle+|\text{decayed pieces}\rangle$$ is a fact that follows from quantum mechanics and other tests demonstrating that it's right.
What you would need is a measurement of the probability that $|\psi\rangle$ is found in the state of the type $$a|{\rm undecayed}\rangle + b|{\rm decayed}\rangle$$ i.e. you need a measurement sensitive on the inner product of $|\psi\rangle$ with the superposition state above. However, the superposition state above gets first "collapsed" either into the decayed piece or the undecayed piece at the beginning of the measurement. The measurement may also find something else but I don't believe there is a doable way to avoid the measurement of the "has the particle decayed" at the same moment.