I have been directed to a new, very short paper from Frank Tipler, "Testing Many-Worlds Quantum Theory By Measuring Pattern Convergence Rates", in which we have yet another alleged experimental test for MWI. Specifically, Tipler thinks he can derive the Born probabilities. He starts by distinguishing between the idealized asymptotic scatter of infinitely many measurements (say, in the double-slit experiment) and the growing actual pattern of always-finitely-many measurements, and then uses Bayes to say something quantitative about the rate at which the former approximates the latter. Without having examined the argument in any depth, I am going to predict that if it holds up, it will be possible to reproduce it within a non-MWI framework (e.g. standard quantum measurement theory). But Bayesian many-worlders may wish to look at the details.
I happened upon the website of a Norwegian physicist named Kim Øyhus who independently came to the many-worlds conclusion in 1990. The page strikes me as an unusually good example of epistemic rationality. He starts from a premise ("if the math of quantum mechanics is true,") and moves onto four hypotheses (which cover all possible states of reality, since the fourth hypothesis is, "something else"), figures out testable predictions of each hypothesis, and comes to the conclusion that the Many-Worlds Interpretation is correct.
As far as I can tell, all he does in his experiment is label one of a pair of electrons as the "Observer" and exclaim that Many-World has been proven because this "Observer" electron enters into a superposition with the other electron. The problem is that literally every other interpretation of quantum theory would make the same predictions for this experiment, however you label the electrons.
“Despite the unrivaled empirical success of quantum theory, the very suggestion that it may be literally true as a description of nature is still greeted with cynicism, incomprehension, and even anger.”
-David Deutsch (As seen on Cosmic Variance)
This is one of several shortened indices into the Quantum Physics Sequence.
Macroscopic quantum superpositions, a.k.a. the "many-worlds interpretation" or MWI, was proposed in 1957 and brought to the general attention of the scientific community in 1970. Ever since, MWI has steadily gained in popularity. As of 2008, MWI may or may not be endorsed by a majority of theoretical physicists (attempted opinion polls conflict on this point). Of course, Science is not supposed to be an opinion poll, but anyone who tells you that MWI is "science fiction" is simply ignorant.
When a theory is slowly persuading scientists despite all academic inertia, and more and more graduate students grow up familiar with it, at what point should one go ahead and declare a temporary winner pending new evidence?
Reading through the referenced posts will give you a very basic introduction to quantum mechanics - algebra is involved, but no calculus - by which you may nonetheless gain an understanding sufficient to see, and not just be told, that the modern case for many-worlds has become overwhelming. Not just plausible, not just strong, but overwhelming. Single-world versions of quantum mechanics just don't work, and all the legendary confusingness and mysteriousness of quantum mechanics stems from this essential fact. But enough telling - let me show you.