Actually had this discussion at a pub a few days ago. There is scientific "proof" that something like a soul exists. Look up MacDougall and his death research. In short, he placed dieing patients on a cadaver scale and kept them relaxed until they were about to pass, The patients' weights slowly decreased as they were about to die (assumed by perspiration being evaporated) and at the moment of death, they lost roughly 3/4 of an ounce. He ran this study multiple times and it happened again and again.
Now, since all things are made of matter and have weight, that 3/4 of an ounce could be assumed to be your soul.
Extra things to consider, while breathing the scale didn't move that much so it isn't them exhaling at time of death. And the death rattle generally comes later. Also, the voided bowels at time of death (assuming it happened that second) would stay on the scale so would be included in that final weigh in.