3 For a short introduction to decoherence, see ref.  or any of the classic expositions of decoherent (consistent) histories quantum theory [4—6].
for alternatives a (e.g. the times of sunrise), given H and and further alternatives 3 (e.g. a few earlier positions and orientations of the Earth). The joint probabilities on the right-hand-side of Eq. (18.5) are computed using Eq. (18.4), as described in Section 18.2.
Conditioning probabilities on specific information can weaken their dependence on H and but does not eliminate it. That is because any specific information available to us as human observers (such as a few positions of the Earth) is but a small part of that needed to specify the state of the Universe. The chains of the form given in Eqs. (18.3) that define a few previous positions of the Earth in Eqs. (18.4) and (18.5) involve projections PY that define a previous position to a certain accuracy. These span a very large subspace of the Hilbert space, so that PY depends strongly on For example, to extrapolate present data on the Earth to its position 24 hours from now requires that the probability be high that it moves on a classical orbit in that time and that the probability be low that it is destroyed by a neutron star now racing across the Galaxy at near light speed. Both of these probabilities depend crucially on the nature of the quantum state .
Many useful predictions in physics are of conditional probabilities of the kind discussed in this section. We next turn to the question of whether we should be part of the conditions.
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