As far as I can tell (being a non-physicist), the Transactional Interpretation shares the mathematical simplicity of MWI. And here Kastner and Cramer argue that TI can derive the Born probabilities naturally, whereas MWI is said to need a detour through "the application of social philosophy and decision theory to subjectively defined ‘rational’ observers". So maybe TI is simpler.
The "possibilities" they posit seem quite parallel (pardon the pun) to the multiple worlds or bifurcated observers of MWI, so I don't see the philosophical ad...
I think the short version is that you don't need math that covers the wavefunction collapse, because you don't need the wave function to collapse.
For a longer version, you'd need someone who knows more QM than I do.
In non-relativistic MWI, the evolution of the quantum state is fully described by the Schrodinger equation. In most other interpretations, you need the Schrodinger equation plus some extra element. In Bohmian mechanics the extra element is the guidance equation, in GRW the extra element is a stochastic Gaussian "hit".
In Copenhagen, the extra element is ostensibly the discontinuous wavefunction collapse process upon measurement, but to describe this as complicating the math (rather than the conceptual structure of the theory) is a bit misleading. Whether you're working with Copenhagen or with MWI, you're going to end up using pretty much the same math for making predictions. Although, technically MWI only relies on the Schrodinger equation, if you want to make useful predictions about your branch of the wave function, you're going to have to treat the wave function as if it has collapsed (from a mathematical point of view). So the math isn't simpler than Copenhagen in any practical sense, but it is true that from a purely theoretical point of view, MWI posits a simpler mathematical structure than Copenhagen.
The thing that's always bugged me about the MWI is that it doesn't seem physically sensible. If something isn't physically sensible, than you need to check on your model. This happens all the time in physics - there are so many basic problems where you discard solutions or throw out different terms because they don't make sense. This is the path to successful understanding, rather than stubbornly sticking to your model and insisting that it must be correct.
The impression I get is that, if the math leads you to make a conclusion which seems like physical n...
You say that there are multiple copies of me inside the wavefunction
I do? Well, I can pretend I do, at least.
Is that because there is one of me that splits into many, or were there just parallel mes living separate but similar lives?"
If we want to recover classical choices in cases where there are clear classical analogs, one of you splits into one. If you'd rather follow other intuitions, though, you'll get different answers (see: quantum suicide).
Note that since humans aren't energy eigenstates, there is no general way to get completely "parallel lives" - you always interfere. But because the world is nice and orderly you can get pretty dang close to parallel most of the time.
So far you've used the example "| / > = | | > + | >", which doesn't tell anyone whether they should think of themselves as "/", as "|" and " ", or otherwise answer the question.
Well, it answers the person who asks "But is the line really one component, or is it really two components?" And that answer is that they've gotten their levels confused - number of components is in your description of the line, not in the line.
Which, to make sure I'm being clear, is analogous to how I interpreted Quantumental's sentence "Obviously both overlap and non-overlap cannot be true, they are ontologically different." If we go with a correspondence theory of truth, we run into a problem because there is no overlap or non-overlap out in quantum mechanics that this sentence could correspond to. Instead, the thing that would make it true or false is humans; specifically how they choose what's right when presented with quantum mechanics. Unfortunately, humans are inconsistent, so you immediately run into the problem of how to idealize them.
I get it now. You're saying that the relativism of how one may define one's personal identity is so great that, in a quantum multiverse, even whether you are splitting into multiple selves or not is a matter of how you define yourself.
Still, that's not the end of it, because then we can ask exactly what parts of the wavefunction are "potential person-parts". I may have some freedom to choose whether a particular object, trait, thought, or state of mind that once existed or that could exist is "part of me", but at some level there has t...
http://www.scottaaronson.com/blog/?p=1103
Eliezer's gung-ho attitude about the realism of the Many Worlds Interpretation always rubbed me the wrong way, especially in the podcast between both him and Scott (around 8:43 in http://bloggingheads.tv/videos/2220). I've seen a similar sentiment expressed before about the MWI sequences. And I say that still believing it to be the most seemingly correct of the available interpretations.
I feel Scott's post does an excellent job grounding it as a possibly correct, and in-principle falsifiable interpretation.