Eliezer, I think your (and Robin’s) intuition is off here. Configuration space is so vast, it should be pretty easy for a small blob of amplitude to find a hiding place that is safe from random stray flows from larger blobs of amplitude.
Consider a small blob in my proposed experiment where the number of 0s and 1s are roughly equal. Writing the outcomes on blackboards does not reduce the integrated squared modulus of this blob, but does move it further into “virgin territory”, away from any other existing blobs. In order for it to be mangled by stray flows from larger blobs, those stray flows would somehow have to reach the same neighborhood as the small blob. But how? Remember that in this neighborhood of configuration space, the blackboards have a roughly equal number of 0s and 1s. What is the mechanism that can allow a stray piece of a larger blob to reach this neighborhood and mangle the smaller blob? It can’t be random quantum fluctuations, because the Born probability of the same sequence of 0s and 1s spontaneously appearing on multiple blackboards is much less than the integrated squared modulus of the small blob. To put it another way, by the time a stray flow from a larger blob reaches the small blob, its amplitude would be spread much too thin to mangle the small blob.
Eliezer, I think your (and Robin’s) intuition is off here. Configuration space is so vast, it should be pretty easy for a small blob of amplitude to find a hiding place that is safe from random stray flows from larger blobs of amplitude.
Consider a small blob in my proposed experiment where the number of 0s and 1s are roughly equal. Writing the outcomes on blackboards does not reduce the integrated squared modulus of this blob, but does move it further into “virgin territory”, away from any other existing blobs. In order for it to be mangled by stray flows from larger blobs, those stray flows would somehow have to reach the same neighborhood as the small blob. But how? Remember that in this neighborhood of configuration space, the blackboards have a roughly equal number of 0s and 1s. What is the mechanism that can allow a stray piece of a larger blob to reach this neighborhood and mangle the smaller blob? It can’t be random quantum fluctuations, because the Born probability of the same sequence of 0s and 1s spontaneously appearing on multiple blackboards is much less than the integrated squared modulus of the small blob. To put it another way, by the time a stray flow from a larger blob reaches the small blob, its amplitude would be spread much too thin to mangle the small blob.
This seems like a devastating objection to the mangled worlds idea. Any counterarguments?