The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [130]
Everett’s approach, which he described as “objectively deterministic” with probability “reappearing at the subjective level,” resonated with this strategy. And he was thrilled by the direction. As he noted in the 1956 draft of his dissertation, the framework offered to bridge the position of Einstein (who famously believed that a fundamental theory of physics should not involve probability) and the position of Bohr (who was perfectly happy with a fundamental theory that did). According to Everett, the Many Worlds approach accommodated both positions, the difference between them merely being one of perspective. Einstein’s perspective is the mathematical one in which the grand probability wave of all particles relentlessly evolves by the Schrödinger equation, with chance playing absolutely no role.* I like to picture Einstein soaring high above the many worlds of Many Worlds, watching as Schrödinger’s equation fully dictates how the entire panorama unfolds, and happily concluding that even though quantum mechanics is correct, God doesn’t play dice. Bohr’s perspective is that of an inhabitant in one of the worlds, also happy, using probabilities to explain, with stupendous precision, those observations to which his limited perspective gives him access.
It’s a captivating vision—Einstein and Bohr agreeing on quantum mechanics. But there are pesky details that for more than half a century have convinced many that it’s still too early to sign on. Those who have studied Everett’s thesis generally agree that while his intent was clear—a deterministic theory that to its inhabitants nevertheless appears probabilistic—he didn’t convincingly spell out how to achieve it. For example, much in the spirit of material covered in Chapter 7, Everett sought to determine what a “typical” inhabitant of the many worlds would observe in any given experiment. But (unlike our focus in Chapter 7) in the Many Worlds approach, the inhabitants we need to contend with are all the same person; if you’re the experimenter, they are all you, and collectively they will see a range of different outcomes. So who is the “typical” you?
Inspired by the Zaxtarian scenario, a natural suggestion is to count the number of yous who will see a given result; the outcome seen by the greatest number of yous would then qualify as typical. Or, more quantitatively, define the probability of a result to be proportional to the number of yous who see it. For simple examples, this works: in Figure 8.16, there’s one of you who sees each outcome, and so you peg the odds at 50:50 for seeing one result or the other. That’s good; the usual quantum mechanical prediction is also 50:50, because the probability wave heights at the two locations are equal.
Figure 8.17 The combined probability wave for you and your device encounters a probability wave that has multiple spikes of different magnitudes.
However, consider a more general situation, such as that in Figure 8.17, in which the probability wave heights are unequal. If the wave is a hundred times larger at Strawberry Fields than at Grant’s Tomb, then quantum mechanics predicts that you are a hundred times more likely to find the electron at Strawberry Fields. But in the Many Worlds approach, your measurement still generates one you who sees Strawberry Fields and another you who sees Grant’s Tomb; the odds based on counting the number of yous is thus still 50:50—the wrong result. The origin of the mismatch is clear. The number of yous who see one result or another is determined by the number of spikes in the probability wave. But the quantum