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a coin operated quantum suicide booth

So here we come finally to the quantum suicide booth. I'm getting rid of the "instrumentalism vs realism" title now because I think we've strayed far enough from the original topic that this is pretty tangential. Truth be told, that whole series ended up being a lot of tangential stuff and not a whole lot directly related to the debate between instrumentalism and realism. That's the way things go I guess. But everything is connected, and in surprisingly intricate ways.

So there's this classic thought experiment called the "quantum suicide" experiment, originated by AI researcher Hans Moravec, and developed further by cosmologist Max Tegmark. It's a derivative of the Schrodinger's Cat and Wigner's Friend thought experiments, but not quite as ancient or well known.

The Quantum Suicide experiment is the closest thing we have to an experimental test that distinguishes between Copenhagen and Many Worlds. However, it is very one-sided in that if Many Worlds is correct, you can be certain it is (however only the person performing the experiment can appreciate that certainty, nobody else in the world can). But if Copenhagen is correct, you will die so you will never know which is correct.

The experiment goes something like this: Construct a device with connects the outcome of a truly random quantum observable, similar to the one used in the Schrodginer's Cat experiment, to a lethal device that kills the experimenter. Have the experimenter (you, let's say) repeat this many times in a row. Assuming Many Worlds is true, then what should you expect to happen? Well, in most of the worlds you will die, but there is guaranteed to be at least one world where you survive. You won't experience anything in the worlds where you die, so the rational thing to do would be to expect your next experience will be seeing yourself miraculously survive the experiment many times in a row. If you perform the experiment and witness this, as expected, then you can be pretty sure Many Worlds is true and Copenhagen is false. Unfortunately, if anyone else witnesses this, without being in the machine themselves, you will be unable to convince them that it wasn't just crazy luck or some kind of divine intervention, since neither of the 2 theories predict that they should see you survive that many times in a row. (Many Worlds only predicts that you should see yourself survive, from your own perspective.)

There's a variant of this which leads to something called Quantum Immortality, but that's considered much more controversial, and depends on other assumptions, so we won't get into that. (My personal feelings are that quantum suicide makes sense and would work assuming Many Worlds is correct, but that Quantum Immortality is an exaggeration/distortion of the thought experiment which leads to nonsensical conclusions.)

At work, we've talked about a lot of different versions of the quantum suicide experiment, because it's pretty relevant to themes we want to explore in the movie we're making (or rather, discussing making). And the most interesting version that's come up is one I've decided to call the "coin operated quantum suicide booth". It was proposed by my coworker as a way of attacking some of the assumptions I hold about observer selection (mostly stemming from Nick Bostrom's Self Sampling Assumption). We argued about it for a while, and at some point, he had succeeded in convincing me that I was probably wrong. But then after a lot more thinking about it, I changed my mind and decided I had been right all along, and do not have to give up the Self Sampling Assumption or any of my views on the anthropic principle.

In this version, there is a booth which contains the above described quantum suicide device. But there is also a coin that gets automatically flipped once you step into the booth. If it comes up heads, then after 10 minutes of waiting in the booth, the quantum suicide experiment is performed on you 1 million times in a row in rapid succession. If it comes up tails, then nothing else happens for 10 minutes, and then either way the door opens and you're allowed to walk out (if you're still alive).

Now imagine that your friend bets you that the coin will land on heads. What odds should you be willing to take on that bet? This hinges on what you think the chances are you'll win the bet, assuming you survive and walk out of the booth. Another related way of asking it is: what do you expect to see happening after you walk out of the booth? There are strong arguments to support several things being true here. 1.) you should be extremely certain that if you end up surviving, you will remember the coin coming up tails and you will win the bet. 2.) you should expect that when you walk into the booth, if you look at the coin, you will see it come up heads with 50% chance and tails with 50% chance, and 3.) whether you look at the coin should not affect in any way the chances that it will come up tails, or that you will remember it having come up tails, and 4.) if you do look at the coin while you're still in the booth, and you see heads, you should expect with 100% probability that after you walk out of the booth, you'll remember seeing heads and lose the bet.

The interesting thing about this thought experiment is, that the 4 things above do not seem consistent with each other at first glance. And yet, I do think they are consistent, and if Many Worlds is true and there is any consistent notion of "what to expect to see next", then it implies they are all true. Before you walk into the booth, you should expect you will win the bet. This should be true regardless of whether you intend to look at the coin. If you don't look at the coin, there's nothing more to be said. In nearly all of the worlds where you survive, you do win the bet. If you do choose to look at the coin while you're in the booth, there's a 50% chance you'll see heads and a 50% chance you'll see tails. If you see tails, then you know you have won the bet. If you see heads, then you're in a really weird situation. You should expect now that you will *lose* the bet (even though before you looked at the coin, you thought you would win it). However, a more nuanced thing to say is that you should expect yourself to be killed in nearly all of the branches, and the only one where you survive you'll lose the bet. So therefore, it's useful to be prepared for that one case where you do survive... so be prepared to pay up! It seems as though, if you were really in this situation, you might be a bit afraid to look at the coin. Like it would ruin your chances of winning the bet. Because then there's a 50% chance you'll be in this weird situation thinking you're either going to die or lose the bet. But if you don't look at the coin, you'll never be in that situation. But the illusion here is that looking at the coin has somehow influenced what's going to happen. The only thing it really affects though is whether you know you're about to die and/or lose the bet. If you don't know, then you don't have to deal with as many weird feelings. Although you still know that a lot of your future selves (roughly half of them) will die, and that in some very obscure branch of the multiverse, you will survive but lose the bet. (For simplicity, we can assume that the outcome of the coin itself is chosen based on some other quantum random variable, which could have been determined far ahead of time. If it's a purely classical coin, then I don't think it changes anything about this analysis, but it makes the whole thing a bit more difficult to think about since the outcome is pseudorandom rather than purely random.)

I'd like to write a bit more about the mind/body problem and the anthropic principle. Clearly things like cloning and the quantum suicide experiments described here tie in heavily to that, and call into question how to tie consciousness (in the sense of subjective personal experience or identity) to physical copies of our bodies. If nobody has written up a paper on this coin operated quantum suicide booth, I'm thinking it might be worthwhile.

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