• Choose a category
• All
• Classic-Fiction

By Root 1994 0

a scientist gains immediate access to the result of his or her experiment, quantum probability seems in danger of being squeezed out of the picture. (For a detailed discussion see David Albert, “Probability in the Everett Picture” in Many Worlds: Everett, Quantum Theory, and Reality, eds. Simon Saunders, Jonathan Barrett, Adrian Kent, and David Wallace (Oxford: Oxford University Press, 2010) and “Uncertainty and Probability for Branching Selves,” Peter Lewis, philsciarchive.pitt.edu/archive/00002636.) A final issue of relevance to Vaidman’s suggestion and also to this type of ignorance probability is this: when I flip a fair coin in the familiar context of a single universe, the reason I say there’s a 50 percent chance the coin will land heads is that while I’ll experience only one outcome, there are two outcomes that I could have experienced. But let me now close my eyes and imagine I’ve just measured the position of the somber electron. I know that my detector display says either Strawberry Fields or Grant’s Tomb, but I don’t know which. You then confront me. “Brian,” you say, “what’s the probability that your screen says Grant’s Tomb?” To answer, I think back on the coin toss, and just as I’m about to follow the same reasoning, I hesitate. “Hmmm,” I think. “Are there really two outcomes that I could have experienced? The only detail that differentiates me from the other Brian is the reading on my screen. To imagine that my screen could have returned a different reading is to imagine that I’m not me. It’s to imagine I’m the other Brian.” So even though I don’t know what my screen says, I—this guy talking in my head right now—couldn’t have experienced any other outcome; that suggests that my ignorance doesn’t lend itself to probabilistic thinking.

11. Scientists are meant to be objective in their judgments. But I feel comfortable admitting that because of its mathematical economy and far-reaching implications for reality, I’d like the Many Worlds approach to be right. At the same time, I maintain a healthy skepticism, fueled by the difficulties of integrating probability into the framework, so I’m fully open to alternative lines of attack. Two of these provide good bookends for the discussion in the text. One tries to develop the incomplete Copenhagen approach into a full theory; the other can be viewed as Many Worlds without the many worlds.

The first direction, spearheaded by Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber, tries to make sense of the Copenhagen scheme by changing Schrödinger’s math so that it does allow probability waves to collapse. This is easier said than done. The modified math should barely affect the probability waves for small things like individual particles or atoms, since we don’t want to change the theory’s successful descriptions in this domain. But the modifications must kick in with a vengeance when a large object like a piece of laboratory equipment comes into play, causing the commingled probability wave to collapse. Ghirardi, Rimini, and Weber developed math that does just that. The upshot is that with their modified equations, measuring does indeed make a probability wave collapse; it sets in motion the evolution pictured in Figure 8.6.

The second approach, initially developed by Prince Louis de Broglie back in the 1920s, and then more fully decades later by David Bohm, starts from a mathematical premise that resonates with Everett. Schrödinger’s equation should always, in every circumstance, govern the evolution of quantum waves. So, in the de Broglie–Bohm theory, probability waves evolve just as they do in the Many Worlds approach. The de Broglie–Bohm theory goes on, however, to propose the very idea I emphasized earlier as being wrongheaded: in the de Broglie–Bohm approach, all but one of the many worlds encapsulated in a probability wave are merely possible worlds; only one world is singled out as real.

To accomplish this, the approach jettisons the traditional quantum haiku of wave or particle (an electron is a wave until it’s measured, whereupon it reverts to being a particle)