Halc said:
Far more likely than this 'improbability drive' scenario (from Hitchhiker's guide) you describe is a sort of Boltzmann brain scenario where a small system somewhere (much smaller than a planet) is by chance put into a state best explained by a history of dinosaurs and such despite the nonexistence of them in actual history.
Just to clarify the notion of a history containing or not containing dinosaurs, since there are two notions of "not containing dinosaurs".
Consider a measurement scenario similar to one I described earlier, but a bit simpler: We have a particle ##s## prepared in state ##|Z^+\rangle\langle Z^+|##, and device ##M## that measures the spin-##X## of ##s##. Like before, we consider two times: one before measurement and one after. So we have a history space ##\mathcal{H}_{t_1}\odot\mathcal{H}_{t_2}## and, at each time, a state space that is a product of the particle and device state space ##\mathcal{H}_{t_i} = \mathcal{S}_{t_i}\otimes\mathcal{M}_{t_i}##. Now consider two incompatible sets of consistent histories ##\mathcal{F}_1## and ##\mathcal{F}_2##.
##\mathcal{F}_1##
\begin{eqnarray*}
[X^+]\odot [M^+]\\
[X^-]\odot [M^+]\\
[X^+]\odot [M^-]\\
[X^-]\odot [M^-]
\end{eqnarray*}##\mathcal{F}_2##
\begin{eqnarray*}
[Z^+]&\odot& [M^+]\\
[Z^+]&\odot& [M^-]\\
[Z^-]&\odot& I_{\mathcal{H}_{t_2}}
\end{eqnarray*}
Now let's say the device produces a datum ##M^+##. Notice the set ##\mathcal{F}_1## contains the history ##[X^-]\odot [M^+]##, which will have a probability that is small but not exactly 0. Equivalently We can compute the conditional probability ##P(X^-|M^+) \approx0##. This implies the chance that the particle has spin ##X^-## at time ##t_1## and the device produces the seemingly contrary datum ##M^+## is small but not exactly zero, meaning there is a very very very slight chance that the datum produced by the device does not match the property it is supposed to record. This is analogous to the improbable history that asserts dinosaurs never existed even though there's a fossil record that heavily implies they did. So, using this analogous set, we can conclude that it is very highly probable that dinosaurs existed if we observe fossils of them.
Now consider ##\mathcal{F}_2##. This set contains assertions about spin-##Z## of the particle at ##t_1##, so we can't interpret an outcome like ##M^+## as a measurement of spin-##X## using this set, because properties like ##X^+## and ##X^-## are indiscussible in this set. It is sets like these that Dowker and Kent use to argue CH implies solipsism. Note that, in this set, no history contains spin ##X^+##, and at least one of them has to be the history that occurred. So by selecting ##\mathcal{F}_2##, we have guaranteed that ##X^+## doesn't exist. Similarly, we could select a set that doesn't contain statements about dinosaurs in any history, and therefore erase them from existence. Where have we gone wrong?
The subtlety is that histories like ##[Z^+]\odot [M^+]## are *not* analogous to dinosaurs not existing in spite of records. In histories like these, dinosaurs are indiscussible. The set ##\mathcal{F}_2## does not guarantee that dinosaurs don't exist. Instead it is a set that is not suitable for discussing the existence of dinosaurs.
