Algernoq comments on timeless quantum immortality - Less Wrong Discussion
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The 20th-century physicists speculated a lot about it. Schrodinger's Cat, the Wigner's Friend problem, etc. But in the absence of a test for consciousness they mostly went on to other things.
I've never heard that it occurred to any of them (aside from Hugh Everett) that quantum mechanics might imply something like quantum immortality, though.