The simplest proof I’ve seen is actually of my own devising, though I’m pretty sure others have come up with it before. Suppose the general framework is right, but there’s some superlinear term somewhere. Essentially, it changes things if any one component gets big—like an absolute amplitude of 1⁄2 or something. And these components can be any of the usual observable variables we’d have—distances between particles, momenta, etc.
Based just on the general framework, the individual components of the wavefunction get very small very quickly. The system decoheres into so many tiny blobs in configuration space that none of them are dense enough for those superlinear terms to be a big deal. And I don’t mean we could prepare a highly concentrated state either. Right there at the Big Bang, the superlinear components could be doing something important, but a few Planck times later they’d be a minor deal, and a millisecond later there’s no conceivable experimental apparatus that one could build that would ever detect their effect.
If there are nonlinearities that do have effects to the present day, they have to have been shepherding the wavefunction in a highly specialized way to prevent this sort of thing from happening. Mangled worlds might do it, but I have low confidence in it.
Cool, I’ve thought of that too. The problem with this approach is that it’s not obvious how to apply the Born rule or whether it must be revised. Apparently Weinberg wrote a paper on something similar, but I’ve never been able to find it.
Hmm. I see what you mean—you can end up with a sort of sleeping beauty paradox, where some branches remain more concentrated than others, and over time their ‘probabilities’ grow or shrink retroactively.
I don’t see that being a fundamental issue of dynamics, but rather of our ability to interpret it. If the Born Rule is an approximation that applies except at the dawn of time, I’m okay with that.
I don’t see that being a fundamental issue of dynamics, but rather of our ability to interpret it. If the Born Rule is an approximation that applies except at the dawn of time, I’m okay with that.
Yeah, that’s what I meant by ‘revised’. I don’t even know if it’s possible to find an approximation that behaves sanely. Last time I thought about this, I thought we’d want to avoid the sort of situation you mentioned, but I’ve been thinking about the anthropic trilemma post and now I’m leaning toward the idea that we shouldn’t exclude it a priori.
The simplest proof I’ve seen is actually of my own devising, though I’m pretty sure others have come up with it before. Suppose the general framework is right, but there’s some superlinear term somewhere. Essentially, it changes things if any one component gets big—like an absolute amplitude of 1⁄2 or something. And these components can be any of the usual observable variables we’d have—distances between particles, momenta, etc.
Based just on the general framework, the individual components of the wavefunction get very small very quickly. The system decoheres into so many tiny blobs in configuration space that none of them are dense enough for those superlinear terms to be a big deal. And I don’t mean we could prepare a highly concentrated state either. Right there at the Big Bang, the superlinear components could be doing something important, but a few Planck times later they’d be a minor deal, and a millisecond later there’s no conceivable experimental apparatus that one could build that would ever detect their effect.
If there are nonlinearities that do have effects to the present day, they have to have been shepherding the wavefunction in a highly specialized way to prevent this sort of thing from happening. Mangled worlds might do it, but I have low confidence in it.
Cool, I’ve thought of that too. The problem with this approach is that it’s not obvious how to apply the Born rule or whether it must be revised. Apparently Weinberg wrote a paper on something similar, but I’ve never been able to find it.
Hmm. I see what you mean—you can end up with a sort of sleeping beauty paradox, where some branches remain more concentrated than others, and over time their ‘probabilities’ grow or shrink retroactively.
I don’t see that being a fundamental issue of dynamics, but rather of our ability to interpret it. If the Born Rule is an approximation that applies except at the dawn of time, I’m okay with that.
Yeah, that’s what I meant by ‘revised’. I don’t even know if it’s possible to find an approximation that behaves sanely. Last time I thought about this, I thought we’d want to avoid the sort of situation you mentioned, but I’ve been thinking about the anthropic trilemma post and now I’m leaning toward the idea that we shouldn’t exclude it a priori.