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First of all, I disagree that the negative time solution can be removed using math; the math will tell you that the solution is perfectly valid.
Secondly, yes, there are cases like in statistical mechanics or basic QM where the theory isn't that intuitive, dealing with huge numbers of particles (as in SM) or dealing with position probabilities (as in QM), but where the process makes sense (I can grok it).
But these theories have clear interpretations in terms of observables; SM has a systematic justification in terms of physical intuition (in terms of the preferred configurations being those with the most probability, or something of that nature), and QM develops right from the beginning how the wave-function picture can be seen as a generalization of the classical picture (positions directly become position operators, as with momenta and so on). There's no such obvious justification for the MWI, in my mind; the linkage between there being many branches of the solution, and there being many universes, is weakly justified at best.
By "physically sensible," what do you mean? When I say that, I usually mean something that my brain is good at modeling,
It's hard to put my finger on this exactly. To me, physically sensible just means it sounds reasonable under the context of observations and everything else that we know. In this specific case, the idea of infinitely many universe branches constantly forking off doesn't seem physically sensible to me when all we observe is a single universe.
In what sort of situation would you expect a correct theory to not be physically sensible?
This just happens all the time. For example, to get the free-fall time for a falling object, you have to take a quadratic root of an expression, which in principle gives a "negative time" root/solution. This solution is obviously nonsense, so you just discard it and don't pay attention to it, but you don't conclude that the theory is wrong.
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 nonsense, then you ought to trust your gut, rather than trusting the math. MWI sounds like nonsense, and completely physically implausible, and that's far more convincing to me than claims that "the math must make it so."
Yes, I am very familiar with this kind of experience. I think the point about singular epiphanies of this sort is that they are always too brittle and inflexible to carry you on in any meaningful, long-term sort of way. Two further comments:
The realization of "epiphany addiction" it itself a sort of epiphany, in the same sense that this discussion is talking about. I'm not sure what the punchline of -that- should be, except maybe to say, there doesn't seem to ever be any such "magic bullets" in terms of personal understanding ... . Yes, this may seem strange.
This whole idea and discussion draw to mind some closely related ideas from eastern (buddhistic) philosophy and thinking, which considers in detail the process of self-growth (ideally, samadhi) by means of self-consideration (generally, meditation). Within those lines of thought, there seems to be a general emphasis on this point in terms of attachment and detachment fallacies; the human being naturally tends to attach to certain dogmas, beliefs, fears, etc. always forgetting the fact that such things are not really real in the same sense that objective reality is real. Thus they are largely illusionary and fallacious in nature. I think a buddhist might probably look at this article and say, "oh, yes I agree," and then promptly forget all about it.