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JGWeissman comments on SIA doomsday - Less Wrong
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Here's an idea, based on Quantum Mechanics, by someone who hardly knows any Quantum Mechanics at all -- therefore it's probably complete nonsense. (If it's not nonsense, feel free to name said solution after me. :-)
Doesn't the amplitude of a configuration need to be squared in order to figure out the probability of its observation? And also don't configurations tend to split more than merge? So doesn't that mean that if an amplitude-10 configuration splits to two amplitude-5 configurations, the relative probability of the first configuration is 10^2=100 compared to 5^2 + 5^2=50?
So, to put it differently, don't earlier instances have a greater probability of observation than later instances?
It is the squared magnitude of quantum amplitude that is conserved, not the quantum amplitude itself (which is represented as a complex number). Otherwise, the Born rule would not produce coherent probabilities.
Concretely: A configuration with amplitude 10 (and measure 100) will split its flow into two configurations 7.07 (and hence measure 50 each).
(Of course these are actually blobs whose measure is a multidimensional integral over the amplitude's squared modulus, and we'd be looking at the equivalent of 5 + 5i and 5 - 5i so that they linearly sum to the original 10 while having length 7.07 each, but whatever...)