  We show that the M\"{o}bius function is orthogonal to the Thue-Morse sequence
$t(n)$ taken along the Piatetski-Shapiro numbers $\lfloor n^c \rfloor$ for any
$1 < c < 2$. Previously this property was established for the subsequence along
the squares $t(n^2)$. These are both examples of M\"{o}bius orthogonal
sequences with maximum entropy.
