> Maybe, as the physicist Yakir Aharonov has advocated, our universe has not only a special, low-entropy initial state at the Big Bang, but also a “postselected final state,” toward which the outcomes of quantum measurements get mysteriously "pulled"—an effect that might show up in experiments as ever-so-slight deviations from the Born rule.

Me, me! I know a kind of postselection effect that can be explained on a napkin (though nobody knows if it's actually true). As a bonus, it can affect not just the Born probabilities, but the probabilities of anything you choose, even things that already happened. Here's how it works.

The idea is a variation on anthropic reasoning, originally due to Bostrom (http://www.anthropic-principle.com/preprints/cau/paradoxes.h...) If there's a completely fair quantum coin, and many people over many generations decide to have kids iff the coin comes up heads, then the coin might appear biased to us for anthropic reasons (more people in the heads-world than in the tails-world). You can influence all sorts of things this way, like Bostrom's example of Adam and Eve deciding to have kids iff a wounded deer passes by their cave to provide them with food. (That's if anthropic probabilities work in a certain intuitive way. If they work in the other intuitive way, you get other troubling paradoxes in the same vein. All imaginable options lead to weirdness AFAIK.)

A few years back I spent a long time on such problems, and came up with a simple experiment about "spooky mental powers" that doesn't even involve creating new observers. It's completely non-anthropic and could be reproduced in a lab now, but the person inside the experiment will be deeply troubled. Here's how it goes:

You're part of a ten-day experiment. Every night you get an injection that makes you forget what day it is. Every day you must pick between two envelopes, a red one and a blue one. One envelope contains $1000, the other contains nothing. At the end of the experiment, you go home with all the money you've made over the ten days. The kicker is how the envelopes get filled. On the first day, the experimenters flip a coin to choose whether the red or the blue one will contain $1000. On every subsequent day, they put the money in the envelope that you didn't pick on the first day.

So here's the troubling thing. Imagine you're the kind of person who always picks the red envelope on principle. Just by having that preference, while you're inside the experiment, you're forcing the red envelope in front of you to be empty with high probability! Since your mental states over different days are indistinguishable to you, you can choose any randomized strategy of picking the envelope, and see the result of that strategy as if it already happened. In effect, you're sitting in a room with two envelopes, whose contents right now depend not just on what you'll choose right now, but on what randomized strategy you'll use to choose right now. If that's not freaky, I don't know what is.

Going back to Aaronson's original point, the world as it looks to us might easily contain postselection and other weird things. Reducing everything to microstates is a valid way to look at the universe, but you aren't a microstate. You are an observer, a big complicated pattern that exists in many copies throughout the microstate, and the decisions of some copies might affect the probabilities observed by other copies at other times. The effects of such weirdness are small in practice, but unavoidable if you want a correct probabilistic theory of everything you observe (or a theory of decision-making for programs that can be copied, which is how I arrived at the problem).