The many-worlds interpretation of quantum physics is not untestable. The most elementary demonstration of the non-classical model of reality is confirming evidence of the many-worlds hypothesis.
Any other situation in quantum mechanics, it turns out, can always be explained by saying, 'You remember the case of the experiment with the two holes? It's the same thing.'

Richard Feynman

The multiverse explanation of reality was formulated by Hugh Everett in 1957. Its leading recent exponent is David Deutsch, who has made it accessible to the rest of us in his book The Fabric of Reality (1997).

A great deal of this book is taken up with the nature of scientific method, of information, of explanation, of how hypotheses undergo confirmation, refutation, and evolution. He intertwines the ideas of Darwin and Popper and defends a realist and critical view of truth and explanation. The truth is out there. The universe is real. Our task as scientists and as rational human beings is to explain it.

The two-slit experiment, the simplest demonstration of irreducibly quantum phenomena, shows that there are things that behave like photons in every way -- interception, reflection, path, interference -- and which are totally undetectable except by the interference they cause with the kind of photons we can detect.

This is not the place to go into the slit experiment in detail. Anyway, I want you to read the book. The Fabric of Reality is one of the most important popular scientific books of the age. I thought the whole idea was nonsense before I tackled Deutsch -- but my philosophical training was wrong.

However, the point is: the two-slit experiment shows that real photons behave as if there exist other entities that are exactly like photons, undetectable except for their interaction with real photons. You can call them "shadow" photons, you can go back to mediaeval scholastic terminology and call them photons in posse. Unnecessary semantic quibbles. You can bury your head in the sand, the way the traditional Copenhagen interpretation does.

The simplest explanation is that they're photons.

The simplest explanation for the quantum slit experiment and for all of quantum physics, the most rock-bottom certain theory that has ever been devised, is that there is another shadow universe of photons out there, interacting with the one we can detect.

And when you do the calculations in detail, it's not just one shadow universe, it's not just photons, it's all quantum events. All possible quantum events really happen.

It is the ultimate Copernican dethronement. There is no one "me" in one infinitesimal slice of possibility; all the events possible in the quantum underworld are real, and all the bifurcations in reality they cause. It is not, pace rp, a formalism in equations waiting for observation. It is simpler -- it is a better explanation -- to say that this is all real. There are no good grounds for holding that some possibilities are real and others aren't. There is no privileged reality, no unique observer.

This explanation of why we see the quantum observations we do, is a better theory: it stands up to the alternatives in a critical, evolutionary way. There seem to be two serious alternatives: one of repeated evolution of a bounded cosmos through time or hyper-time (espoused by Lee Smolin in The Life of the Cosmos), and the old search for mathematical constraints that make our present anthropic universe logically necessary.

Neither of these others thoroughly explains what we see. The quantum many-worlds theory does.