This question is not necessarily about the real world, but an imaginary one (which may happen to behave the same as the real one), so i'm not worried about the actual laws of physics, but the philosophical implications of a thought experiment. Also, I'm assuming this world is a consistent one, meaning nothing can be both true and false at the same time, such that this world could theoretically exist, if nothing else, as a computer simulation.
This world is, for every know physical law, the same as ours, except that you can build a perfectly isolated box where you can actually run the Schrödinger's cat experiment. In this world there's also a many worlds interpretation of quantum mechanics, and I want to put it to the test by getting myself into the box and running the experiment.
Let's suppose that, for whatever reason, every time I run the experiment I find myself surviving it. Every time I do so, I'd be twice as confident that the many worlds interpretation (MWI) is right (assuming I ruled out errors in the system). I'll be able to achieve arbitrary certainty by running the experiment as many times as needed. By running it enough times, I'll be more certain about MWI than I can be about any other physical law which we're not 100% sure about, which I suppose are all of them. We can even suppose I built a mechanism that will automatically run the experiment millions of times per second.
If I have a few colleagues waiting for me outside the box, one version of them would see me coming out alive after running it several times. But to them, the chances of seeing this are the same whether MWI is right or not. Seeing me coming out of the box alive, from their point of view, wouldn't make it more likely for the MWI to be true. So they'd really just be hanging around, without hoping to make any discovery regardless of what the result of the experiment is.
Note that what I experienced in the box is nothing the outside observers couldn't imagine. Is not like I had some sort of revelation that cannot be put in words. They know exactly what happened to me, and what it looked like from my point of view. They'd have the same information as I do, but apparently, using the same premises, wouldn't reach the same conclusion, even if we all use the same scientific method and rules of reasoning. So my question-tree would look like:
Would it be right for me to conclude that MWI is real?
- If yes, should my colleagues reach the same conclusion?
- If yes, how come, since seeing me come out alive is as unlikely whether MWI is true or not?
- If no, how could I reach this conclusion while they couldn't if we all have the same information, use the same logic and scientific method?
- If no, then why would I believe any other physical law which is know because a hypothesis H predicts a result R, and every time an experiment is made, the result R is reached, which AFAIK is all of them? Would the fact that I'd die in the ~R case matter? What if I my hypothesis is that holding by breath for 5 seconds won't kill me, and I hold my breath for 5 seconds again and again. Would this be an invalid experiment because I'd be dead if the hypothesis was false?