Peter McCluskey pointed me to a nice explanation by Brian Greene of an experiment that could theoretically distinguish the Copenhagen and Many Worlds interpretations of quantum mechanics. This is from *The Hidden Reality*, ch. 8, endnote 12:

Here is a concrete in-principle experiment for distinguishing the Copenhagen and Many Worlds approaches. An electron, like all other elementary particles, has a property known as

spin. Somewhat as a top can spin about an axis, an electron can too, with one significant difference being that the rate of this spin—regardless of the direction of the axis—is always the same. It is an intrinsic property of the electron, like its mass or its electrical charge. The only variable is whether the spin is clockwise or counterclockwise about a given axis. If it is counterclockwise, we say the electron’s spin about that axis isup; if it is clockwise, we say the electron’s spin isdown. Because of quantum mechanical uncertainty, if the electron’s spin about a given axis is definite—say, with 100 percent certainty its spin is up about the z-axis—then its spin about the x- or y-axis is uncertain: about the x-axis the spin would be 50 percent up and 50 percent down; and similarly for the y-axis.Imagine, then, starting with an electron whose spin about the z-axis is 100 percent up and then measuring its spin about the x-axis. According to the Copenhagen approach, if you find spin-down, that means the probability wave for the electron’s spin has collapsed: the spin-up possibility has been erased from reality, leaving the sole spike at spin-down. In the Many Worlds approach, by contrast, both the spin-up and spin-down outcomes occur, so, in particular, the spin-up possibility survives fully intact.

To adjudicate between these two pictures, imagine the following. After you measure the electron’s spin about the x-axis, have someone fully reverse the physical evolution. (The fundamental equations of physics, including that of Schrödinger, are time-reversal invariant, which means, in particular, that, at least in principle, any evolution can be undone. See

The Fabric of the Cosmosfor an in-depth discussion of this point.) Such reversal would be applied to everything: the electron, the equipment, and anything else that’s part of the experiment. Now, if the Many Worlds approach is correct, a subsequent measurement of the electron’s spin about the z-axis should yield, with 100 percent certainty, the value with which we began: spin-up. However, if the Copenhagen approach is correct (by which I mean a mathematically coherent version of it, such as the Ghirardi-Rimini-Weber formulation), we would find a different answer. Copenhagen says that upon measurement of the electron’s spin about the x-axis, in which we found spin-down, the spin-up possibility was annihilated. It was wiped off reality’s ledger. And so, upon reversing the measurement we don’t get back to our starting point because we’ve permanently lost part of the probability wave. Upon subsequent measurement of the electron’s spin about the z-axis, then, there is not 100 percent certainty that we will get the same answer we started with. Instead, it turns out that there’s a 50 percent chance that we will and a 50 percent chance that we won’t. If you were to undertake this experiment repeatedly, and if the Copenhagen approach is correct, on average, half the time you would not recover the same answer you initially did for the electron’s spin about the z-axis. The challenge, of course, is in carrying out the full reversal of a physical evolution. But, in principle, this is an experiment that would provide insight into which of the two theories is correct.

I’m not a physicist, and I don’t know whether this account is correct. Does anyone dispute it?

Further references on the subject are at Wikipedia.

In any case, such an experiment seems far beyond our reach. But since I’m Bayesian rather than Popperian, I put substantially more probability mass on MWI than Copenhagen even in the absence of definitive experiment. 😉