In another thread the topic of Schroedinger's Cat came up, and specifically the issue of the death of the cat (caused by the radioactive decay of some material, as in the the thought experiment, that leads to a vial of poison being released to the air or whatever which kills the cat).
Another poster said that if you allow the experiment to run, the probability of the radioactive element decaying will be 100%.
I suggested that if you arranged the experiment such that there is a 50% chance of this decay happening over, say, 1 hour, and allowed the experiment to run, that, given that each iteration of the experiment has a 50% chance of not resulting in the cat's death, then while the chance of the cat dying increases over time, it never reaches 1: there is always some chance that the cat will not die.
I tried to demonstrate this by pointing out that while the probability of decay is 75% after 2 hours, in those situations where we look and see that no decay has occurred after 1 hour, there is then a 50% chance that no decay will happen in the second hour as well. And symmetry between the first hour and the second hour remains no matter how long we decide to run the experiment: yes the chance of decay increases with time, but it never reaches 1, just as if you flip a coin once/hour the chances of getting heads increases with time, but never reaches 1: each coin flip is still an independent event with a 50/50 chance of heads/tails.
I may have misunderstood the other poster, for instance in any real set-up the amount of material used will be more than 1 atom. Perhaps we are weighing this material to determine if decay has occurred and thus if some small amount of decay happened in the first hour, but not enough to set off our detector, then the chances of the detector going off in the second hour are higher than in the first. But there will still always be a non-zero chance of not setting off the detector.
In order not to misrepresent his view which I personally had a hard time of understanding, I'll quote him. On the other hand I want to leave him anonymous in case he isn't interested in participating in this thread. This was the bit that started the discussion:
Another poster said that if you allow the experiment to run, the probability of the radioactive element decaying will be 100%.
I suggested that if you arranged the experiment such that there is a 50% chance of this decay happening over, say, 1 hour, and allowed the experiment to run, that, given that each iteration of the experiment has a 50% chance of not resulting in the cat's death, then while the chance of the cat dying increases over time, it never reaches 1: there is always some chance that the cat will not die.
I tried to demonstrate this by pointing out that while the probability of decay is 75% after 2 hours, in those situations where we look and see that no decay has occurred after 1 hour, there is then a 50% chance that no decay will happen in the second hour as well. And symmetry between the first hour and the second hour remains no matter how long we decide to run the experiment: yes the chance of decay increases with time, but it never reaches 1, just as if you flip a coin once/hour the chances of getting heads increases with time, but never reaches 1: each coin flip is still an independent event with a 50/50 chance of heads/tails.
I may have misunderstood the other poster, for instance in any real set-up the amount of material used will be more than 1 atom. Perhaps we are weighing this material to determine if decay has occurred and thus if some small amount of decay happened in the first hour, but not enough to set off our detector, then the chances of the detector going off in the second hour are higher than in the first. But there will still always be a non-zero chance of not setting off the detector.
In order not to misrepresent his view which I personally had a hard time of understanding, I'll quote him. On the other hand I want to leave him anonymous in case he isn't interested in participating in this thread. This was the bit that started the discussion:
Quote:
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The other point made before is that the sum of the probabilities is 100%. So eventually the material does decay and the cat is killed in all worlds. The only way to maintain a 50%-50% ratio on each trial is to replace the radioactive element at each trail. As time for the given element would not start at T=0 but T= the sum of all the other trials. In other words the probability would skew to the cat getting killed. |
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