The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [131]
Everett developed a mathematical argument that was meant to address this mismatch; many others have since pushed it further.9 In broad strokes, the idea is that in calculating the odds of seeing one or another outcome, we should place ever-less weight on universes whose wave heights are ever smaller, as depicted symbolically in Figure 8.18. But this is perplexing. And controversial. Is the universe in which you find the electron at Strawberry Fields somehow a hundred times as genuine, or a hundred times as likely, or a hundred times as relevant as the one in which you find it at Grant’s Tomb? These suggestions would surely create tension with the belief that every world is just as real as every other.
After more than fifty years, during which distinguished scientists have revisited, revised, and extended Everett’s arguments, many agree that the puzzles persist. Yet it remains seductive to imagine that the mathematically simple, totally bare-bones, profoundly revolutionary Many Worlds approach yields the probabilistic predictions that form the foundation of belief in quantum theory. This has inspired many other ideas, beyond the Zaxtarian-type reasoning, for joining probability and Many Worlds.10
A prominent proprosal comes from a leading group of researchers at Oxford, including, among others, David Deutsch, Simon Saunders, David Wallace, and Hilary Greaves. They’ve developed a sophisticated line of attack that focuses on a seemingly boorish question. If you’re a gambler, and you believe in the Many Worlds approach, what’s the optimum strategy for placing bets on quantum mechanical experiments? Their answer, which they argue for mathematically, is that you’d bet just as Neils Bohr would. When speaking of maximizing your return, these authors have in mind something that would have sent Bohr into a tizzy—they’re considering an average over the many inhabitants of the multiverse who claim to be you. But even so, their conclusion is that the numbers that Bohr and everyone since have been calculating and calling probabilities are the very numbers that should guide how you wager. That is, even though quantum theory is fully deterministic, you should treat the numbers as if they were probabilities.
Some are convinced that this completes Everett’s program. Some are not.
The lack of consensus on the crucial question of how to treat probability in the Many Worlds approach is not all that unexpected. The analyses are highly technical and also deal with a topic—probability—that is notoriously tricky even outside its application to quantum theory. When you roll a die, we all agree that you have a 1 in 6 chance of getting a 3, and so we’d predict that over the course of, say, 1,200 rolls the number 3 will turn up about 200 times. But since it’s possible, in fact likely, that the number of 3s will deviate from 200, what does the prediction mean? We want to say that it’s highly probable that ⅙th of the outcomes will be 3s, but if we do that, then we’ve defined the probability of getting a 3 by invoking the concept of probability. We’ve gone circular. That’s just a small taste of how the issues, beyond their intrinsic mathematical complexity, are conceptually slippery. Throw into the mix the added Many Worlds intricacy of “you” no longer referring to a single person, and it’s no wonder researchers find ample points of contention. I have little doubt that full clarity will one day emerge, but not yet, and perhaps not for some time.
Figure 8.18 (a) A schematic illustration of the evolution, dictated by Schrödinger’s equation, of the combined probability wave for all the particles making up you and the measuring device, when you measure the position of an electron. The electron’s own probability wave is spiked at two locations, but with unequal wave heights.
Figure 8.18 (b) Some proposals suggest