Thanks to Eliezer’s QM series, I’m starting to have enough background to understand Robin’s paper (kind of, maybe). And now that I do (kind of, maybe), it seems to me that Robin’s point is completely demolished by Wallace’s points about decoherence being continuous rather than discrete and therefore there being no such thing as a number of discrete worlds to count.
There seems to be nothing to resolve between the probabilities given by measure and the probabilities implied by world count if you simply say that measure is probability.
Eliezer objects. We’re interpreting. We’re adding something outside the mathematics.
I fail to see the problem.
If we’re to accept that particles moving like billiard balls are an illusion, and configuration space is real, and blobs of amplitude are real, and time evolution of amplitude within configuration space according to the wave equations is real, and that configurations and amplitude and wave equations are fundamental parts of reality, because that’s the best model we’ve come up with that agrees with experimental observation… why not accept that the modulus-squared law is real and fundamental, too?
It certainly agrees with experimental observations, and doesn’t seem any less desirable a part of our model of reality than configurations, amplitude blobs, and wave equations.
I wish someone would explain the problem more clearly, although if Eliezer’s explanations so far haven’t cleared it up for me yet, perhaps nothing will.
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”.
Thanks to Eliezer’s QM series, I’m starting to have enough background to understand Robin’s paper (kind of, maybe). And now that I do (kind of, maybe), it seems to me that Robin’s point is completely demolished by Wallace’s points about decoherence being continuous rather than discrete and therefore there being no such thing as a number of discrete worlds to count.
There seems to be nothing to resolve between the probabilities given by measure and the probabilities implied by world count if you simply say that measure is probability.
Eliezer objects. We’re interpreting. We’re adding something outside the mathematics.
I fail to see the problem.
If we’re to accept that particles moving like billiard balls are an illusion, and configuration space is real, and blobs of amplitude are real, and time evolution of amplitude within configuration space according to the wave equations is real, and that configurations and amplitude and wave equations are fundamental parts of reality, because that’s the best model we’ve come up with that agrees with experimental observation… why not accept that the modulus-squared law is real and fundamental, too?
It certainly agrees with experimental observations, and doesn’t seem any less desirable a part of our model of reality than configurations, amplitude blobs, and wave equations.
I wish someone would explain the problem more clearly, although if Eliezer’s explanations so far haven’t cleared it up for me yet, perhaps nothing will.
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”.