From “The flawed multiverse,” Alastair I M Rae’s Physicsworld (Sep 22, 2011) review of David Deutsch’s The Beginning of Infinity: Explanations that Transform the World:
According to the quantum-information theorist David Deutsch, our modern understanding of how the world works has provided us with “good explanations” that open up essentially infinite possibilities for future progress. One of these explanations is the idea of the quantum multiverse, which Deutsch discussed in the May issue of Physics World (pp34–38, print version only) and to which he devotes a chapter in his book The Beginning of Infinity.
I believe the many-worlds theory is open to criticism for reasons other than extravagence. One of these concerns probabilities in a situation where both outcomes occur in parallel. If both options are happening, how can it be meaningful to say that one is more probable than the other – as is experimentally the case if the reflector is not exactly 50/50?
As he described in his Physics World article, Deutsch’s response is to propose that before the measurement, the photon is not just a single particle but is actually an (uncountable) infinity of identical or “fungible” particles. After interacting with the reflector, an infinite number of fungible photons exist in both output channels, but the ratio of these numbers is finite, so that each has a “measure” proportional to the squared modulus of the wavefunction. Even though an observer knows they are going to evolve into two copies of themself, they can apparently assign relative probabilities to which copy they expect to become. These probabilities are given by the Born rule. [Registration required.]
Rae isn’t convinced that this Deutsch fix – or others – resolve the problems, and is put off by the book’s dogmatic tone. He comments,
Deutsch willingly accepts that much of his inspiration comes from the work of Karl Popper, whose mantra “we have a duty to be optimistic” clearly underlies his thinking. However, he would have done well to remember that Popper was often dogmatic, to the point where some wags said that his book The Open Society and its Enemies should have been called “The Open Society by one of its Enemies”!