# shminux comments on Group rationality diary, 6/11/12 - Less Wrong Discussion

2 12 June 2012 06:39AM

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Comment author: 17 June 2012 10:25:15PM 3 points [-]

The other day Patrick mentioned to me on #lesswrong that one of the multiverses Briane Greene talks in his book Hidden Reality... is of the MWI type. So I looked through the book, and here is the relevant passage:

Over the years, a number of researchers including Neill Graham; Bryce DeWitt; James Hartle; Edward Farhi, Jeffrey Goldstone, and Sam Gutmann; David Deutsch; Sidney Coleman; David Albert; and others, including me, have independently come upon a striking mathematical fact that seems central to understanding the nature of probability in quantum mechanics. For the mathematically inclined reader, here’s what it says: Let be the wavefunction for a quantum mechanical system, a vector that’s an element of the Hilbert space H. The wavefunction for n-identical copies of the system is thus. Let A be any Hermitian operator with eigenvalues αk, and eigenfunctions. Let Fk(A) be the “frequency” operator that counts the number of timesappears in a given state lying in. The mathematical result is that lim. That is, as the number of identical copies of the system grows without bound, the wavefunction of the composite system approaches an eigenfunction of the frequency operator, with eigenvalue. This is a remarkable result.

Now, this makes me update more toward the statement "MWI does not require any extra assumptions beyond the Schroedinger equation", though not all the way there, because it postulates "infinitely many identical copies of the system", which is still a separate postulate. There is a further problem with this. Brian Greene again, now for a two-state system:

So from the standpoint of observers (copies of the experimenter) the vast majority would see spin-ups and spin-downs in a ratio that does not agree with the quantum mechanical predictions. Only the very few terms in the expansion of that have 98 percent spin-ups and 2 percent spin-downs are consistent with the quantum mechanical expectation; the result above tells us that these states are the only ones with nonzero Hilbert space norm as n goes to infinity. In some sense, then, the vast majority of terms in the expansion of(the vast majority of copies of the experimenter) need to be considered as “non existent.” The challenge lies in understanding what, if anything, that means.

This is a standard problem in MWI, but still, there are some hints that MWI may be a part of the next step in the quantum theory, when it finally happens.

Comment author: 19 June 2012 09:10:10AM 0 points [-]

Were some characters dropped in the block quotes? It looks like some variable names went missing.

Comment author: 19 June 2012 03:06:26PM 0 points [-]

Sorry, this is digitized from a printed book.