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JGWeissman comments on SIA doomsday - Less Wrong
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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...)