First, let me say beautifully clear explanation of what MWI is and especially what questions it needs to answer.
Except, a peak can have a spread in configuration space. A single peak can be more like a “ridge” stretching between configurations which are classically inconsistent. This already poses problems of interpretation, as does the lack of clear boundaries to a peak… Are we going to say that a world consists of any portion of the wavefunction centered on a peak—a local maximum—and bounded by regions where the gradient is flat??
I don’t think this is any more unreasonable than talking about firing two separate localized wave-packets at each other and watching them interfere, even if we don’t have a specific fixed idea of what in full generality counts as a “wave-packet”. Typically, of course, for linear wave equations we’d use Gaussians as models, but I don’t think that’s more than a mathematically convenient exemplar.
For non-linear models, (e.g. KdV) we have soliton solutions that have rather different properties, such as being self-focusing, rather than spreading out. I guess I don’t see why it matters whether you have an exact definition for “world” or not—so long as you can plausibly exhibit them.
The question in my mind is whether evolution on configuration space preserves wave-packet localization, or under what conditions they could develop. I find it hard to even formalize this, but given that we have a linear wave-equation, I would tend to doubt they do.
e.g. to do with relativity
Of course relativity will be an issue. QM is not Einsteinian relativistic, only Galilean (relabeling phases properly gives a Galilean boost), and that’s baked into the standard operators and evolution.
First, let me say beautifully clear explanation of what MWI is and especially what questions it needs to answer.
I don’t think this is any more unreasonable than talking about firing two separate localized wave-packets at each other and watching them interfere, even if we don’t have a specific fixed idea of what in full generality counts as a “wave-packet”. Typically, of course, for linear wave equations we’d use Gaussians as models, but I don’t think that’s more than a mathematically convenient exemplar. For non-linear models, (e.g. KdV) we have soliton solutions that have rather different properties, such as being self-focusing, rather than spreading out. I guess I don’t see why it matters whether you have an exact definition for “world” or not—so long as you can plausibly exhibit them. The question in my mind is whether evolution on configuration space preserves wave-packet localization, or under what conditions they could develop. I find it hard to even formalize this, but given that we have a linear wave-equation, I would tend to doubt they do.
Of course relativity will be an issue. QM is not Einsteinian relativistic, only Galilean (relabeling phases properly gives a Galilean boost), and that’s baked into the standard operators and evolution.