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The Sciences

Thought experiments

Cosmic VarianceBy Sean CarrollDecember 31, 2005 12:35 AM

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You are offered a deal in which you are asked to flip a coin ten times. If any one of the flips comes up tails, you are swiftly and painlessly killed. If it comes up heads ten times in a row, you are given a banana. Do you take the deal? For the purposes of this thought experiment, we may assume it is a perfectly fair coin, and that you like bananas, although not any more so than would generally be considered healthy. We may also assume for simplicity that your life or death is of absolutely no consequence to anyone but yourself: you live in secret on a deserted island, isolated from contact with the outside world, where you have everything you need other than bananas. We may finally assume that we know for certainty that there is no afterlife; upon death, you simply cease to exist in any form. So, there is an approximately 99.9% chance that you will be dead, which by hypothesis implies that you will feel no regrets or feelings of disappointment. And if you survive, you get a banana. What do you think? Now change the experiment a little. Instead of flipping a coin, you measure the x-component of the spin of an electron that has been prepared in an eigenstate of the y-component of the spin; according to the rules of quantum mechanics, there is an even chance that you will measure the x-component of the spin to be up or down. You do this ten times, with ten different electrons, and are offered the same wager as before, with spin-up playing the role of "heads" for the coin. The only difference is that, instead of a classical probability, we are dealing with branching/collapsing wavefunctions. I.e., if you believe in something like the many-worlds interpretation of quantum mechanics, there will always be a branch of the wavefunction of the universe in which you continue to exist and now have a banana. Do you take the deal?

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