It happens all the time, actually, in our universe. Out in space, particles appear spontaneously. They always appear in pairs, which, most of the time, immediately annihilate with each other and leave no trace. Near black holes, however, a particle might be pulled into a black hole and the matching one might fly out, which is known as 'Hawkings Radiation'. This is also the reason why quantum mechanics can't be practically observed in the macroscopic scale. The random particles generated by the universe cause the superposition states to collapse almost instantly.