why not accept that the modulus-squared law is real and fundamental, too?
Reading through this, and Hanson’s quick overview page of mangled worlds, I was wondering the same thing myself. For some reason though, seeing you ask the question I hadn’t quite verbalized put the answer right on the tip of my tongue: for the same reason Einstein was so sure of General Relativity. The modulus squared law conflicts with a regularity in the form that the fundamental laws seem to take, specifically their linear evolution, and Eliezer puts stock in that regularity. In fact, he does so sufficiently to let him elevate any theory which accounts for the data while holding the regularity far above those that don’t, similar to how Einstein picked GR out of hypothesis space.
The benefit of the mangled worlds interpretation is that while the universe-amplitude-blobs do have measure (a non-linear element), it is irrelevant to what actually happens. It really only comes into play when trying to understand the interaction between the universe-amplitude-blobs, but it doesn’t play a part in actually describing that interaction. For example, the possible mangling of a world of small measure would be described by normal linear quantum evolution, but since the calculations are not very nice, we can determine whether it would be mangled using that measure. Thus, we are using the measure as a mathematical shortcut to determine generalized behavior, but all evolution is linear, and observations can be explained without the extra hypothesis that “measure is probability”.
Reading through this, and Hanson’s quick overview page of mangled worlds, I was wondering the same thing myself. For some reason though, seeing you ask the question I hadn’t quite verbalized put the answer right on the tip of my tongue: for the same reason Einstein was so sure of General Relativity. The modulus squared law conflicts with a regularity in the form that the fundamental laws seem to take, specifically their linear evolution, and Eliezer puts stock in that regularity. In fact, he does so sufficiently to let him elevate any theory which accounts for the data while holding the regularity far above those that don’t, similar to how Einstein picked GR out of hypothesis space.
The benefit of the mangled worlds interpretation is that while the universe-amplitude-blobs do have measure (a non-linear element), it is irrelevant to what actually happens. It really only comes into play when trying to understand the interaction between the universe-amplitude-blobs, but it doesn’t play a part in actually describing that interaction. For example, the possible mangling of a world of small measure would be described by normal linear quantum evolution, but since the calculations are not very nice, we can determine whether it would be mangled using that measure. Thus, we are using the measure as a mathematical shortcut to determine generalized behavior, but all evolution is linear, and observations can be explained without the extra hypothesis that “measure is probability”.