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By Root 1990 0

I had it too. But the reasoning runs completely counter to the Many Worlds approach. Many Worlds practices minimalist architecture. Probability waves simply evolve by Schrödinger’s equation. That’s it. To imagine that one of the copies of you is the “real” you is to slip in through the back door something closely akin to Copenhagen. Wave collapse in the Copenhagen approach is a brutish means for making one and only one of the possible outcomes real. If in the Many Worlds approach you imagine that one and only one of the yous is really you, you’re doing the same thing, just a little more quietly. Such a move would erase the very reason for introducing the Many Worlds scheme. Many Worlds emerged from Everett’s attempt to address the failings of Copenhagen, and his strategy was to invoke nothing beyond the battle-tested Schrödinger equation.

This realization shines an uncomfortable light on the Many Worlds approach. We have confidence in quantum mechanics because experiments confirm its probabilistic predictions. Yet, in the Many Worlds approach, it’s hard to see how probability even plays a role. How, then, can we tell the third kind of story, the one that should provide the basis of our confidence in the Many Worlds scheme? That’s the quandary.

On reflection, it’s not surprising that we’ve bumped into this wall. There’s nothing at all chancy in the Many Worlds approach. Waves simply evolve from one shape to another in a manner described fully and deterministically by Schrödinger’s equation. No dice are thrown; no roulette wheels are spun. By contrast, in the Copenhagen approach, probability enters through the hazily defined measurement-induced wave collapse (again, the larger the wave’s value at a given location, the larger the probability that the collapse will put the particle there). That’s the point in the Copenhagen approach where “dice throwing” makes an appearance. But since the Many Worlds approach abandons collapse, it abandons the traditional entry point for probability.

So, is there a place for probability in the Many Worlds approach?

Probability and Many Worlds

Everett surely thought there was. The bulk of his 1956 draft dissertation, as well as the truncated 1957 version, was devoted to explaining how to incorporate probability in the Many Worlds approach. But a half century later, the debate still rages. Among those physicists and philosophers who spend their professional lives puzzling over the issue, there is a wide range of opinions on how, and whether, Many Worlds and probability come together. Some have argued that the problem is insoluble, and so the Many Worlds approach should be discarded. Others have argued that probability, or at least something that masquerades as probability, can indeed be incorporated.

Everett’s original proposal provides a good example of the difficult points that arise. In everyday settings, we invoke probability because we generally have incomplete knowledge. If, when a coin is tossed, we know enough details (the coin’s precise dimensions and weight, precisely how the coin was thrown, and so on), we’d be able to predict the outcome. But since we generally don’t have that information, we resort to probability. Similar reasoning applies to the weather, the lottery, and every other familiar example where probability plays a role: we deem the outcomes chancy only because our knowledge of each situation is limited. Everett argued that probabilities find their way into the Many Worlds approach because an analogous ignorance, from a thoroughly different source, necessarily creeps in. Inhabitants of the Many Worlds only have access to their own single world; they do not experience the others. Everett argued that with such a limited perspective comes an infusion of probability.

To get a feel for how, leave quantum mechanics for a moment and consider an imperfect but helpful analogy. Imagine that aliens from the planet Zaxtar have succeeded in building a cloning machine that can make identical copies of you, me, or anyone. Were you to step into the cloning machine, and were two