Looks like an appeal to the divine, in that it doesn't explain anything but does push the question up a level.
"Why does something exist?" "God did it." "Uh, ok, why does God exist?" "Dunno, just does." <- sure seems like you could have simply applied that last answer to the first question and it'd be exactly as useful and valid.
"Why does something exist?" "The set of all possible wave states exists and behaves such-and-such way" "OK, but why does that exist and why does it do that?" "Dunno, just does". <- Ditto.
There is something about this that at least partially satisfies the question, in that it simplifies as you go one level up.
With the "God did it" explanation, something vastly more complex and inscrutable is required (i.e. God) to make the explanation work. With this explanation, there is but a simple wave that splits on its possible oscillations. Our existence is on one of these.
No explanation will ever find the "bottom turtle." There will always be space for another "why?" question. The interesting part is probably more to do with the "asker" this question rather than the answer to it. That we have this capacity to think abstractly about this is, to me, more mind-blowing than the nature of existence itself.
The only thing problematic about “appeals to the divine” or other explanations that “push the question up a level” is if part of the explanation is the prohibition of “where did that thing come from?” or “why is it this way and not some other way?”
But pushing things up a level is actually the only option we have for good explanations. For any explanation about anything whatsoever, you should always be able to ask “why is it this way rather than some other way?” It’s not some paradox or contradiction that there will never be an end to this series of explanations and questions, and any claim that there is an end is the bad kind of “appeal to the divine”!!
True if the level you shift it up to has some further explanatory value and/or can be demonstrated or proven in some fashion. If it's just "well, it might be this thing that we can't prove" then, until you've turned that notion into something you can test or at least support with observations, it's just "god did it".
I think "there's something rather than nothing because the set of all possible waves exists... like, somewhere" is roughly identical to "god did it", as opposed to, say, a hypothesis that things fall and planets orbit due to a universal force that causes matter to attract other matter, even if both just prompt another "why?" You can go do stuff with the latter—not so much with the former, which is more of a dodge than even a partial explanation.
A good test might be whether you can apply the answer to any "why?" that lacks an existing answer, with exactly the same utility and validity in every case. Take the example of the question suggested by the explanation of universal gravitation:
"OK, why does gravity exist, then?"
"God did it / that's just what our little corner of the set of all possible waves happens to look like"
There's simply no specificity to them, and they amount to "just because".
From a mathematical/algorithmic point of view, you could define a good explanation as a sort of compression process: on one hand, you have observations, data to explain, totalling a certain number of bits. On the other hand, you have a process or algorithm that can generate these observations, and if that process can be described in less bits than the original observations, then you have a "good explanation". For example, our current theories for the laws of physics are excellent explanations, because they can explain a virtually infinite number of real observations from finite information.
On the other hand, if the observations are truly random, then in general no shorter process can produce them, so there can be no good explanation for them. And the interesting thing is that if every good explanation compresses the original observations at least one bit further (otherwise they would not be good), there must be a point where the result is as short as it could possibly be. At this point, the series of good explanations would have to end (although I believe that it is undecidable to know when the end is reached).
It is also always possible for something that has a good explanation to actually be a brute fact, like the idea that the Earth was created with the appearance of old age: the good explanation would be that it aged, but the truth would be that it didn't.
I don’t think the length of the explanation is very relevant, and finding shorter explanations doesn’t seem like a primary concern. Explanations should be judged on what problems they solve and how well they stand up to criticism and competing explanations. And since I don’t think any explanation can be “final” or “100% true” or “guaranteed” or anything like that, the notion of a shortest possible explanation doesn’t even make much sense.
"Why does something exist?" "God did it." "Uh, ok, why does God exist?" "Dunno, just does." <- sure seems like you could have simply applied that last answer to the first question and it'd be exactly as useful and valid.
"Why does something exist?" "The set of all possible wave states exists and behaves such-and-such way" "OK, but why does that exist and why does it do that?" "Dunno, just does". <- Ditto.