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...)
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...)