  This paper discusses the symmetry of the wave field that lies to the right
and left of a two-sided accelerated mirror in 1 + 1 space and satisfies a
single condition on it. The symmetry is accumulated in the Bogolyubov matrix
coefficients $\alpha$ and $\beta$ that connect the two complete sets of
solutions of the wave equations. The amplitudes of the quantum processes in the
right and left half-spaces are expressed in terms of $\alpha$ and $\beta$ and
are related to each other by transformation (12). Coefficient
$\beta_{\omega'\omega}^*$ plays the role of the source amplitude of a pair of
particles that are directed to opposite sides with frequencies $\omega$ and
$\omega'$ but that are in either the left or the right half-space as a
consequence of the reflection of one of them. Such an interpretation makes
$\beta_{\omega'\omega}^*$ observable and explains the equalities, given by Eq.
(1) and found earlier by Nikishov and author [Zh. Eksp. Teor. Fiz. 108, 1121
(1995)] and by author [Zh. Eksp. Teor. Fiz. 110, 526 (1996)] that the radiation
spectra of a mirror in 1+1 space coincide with those of charges in 3 + 1 space
by the fact that the moment of the pair emitted by the mirror coincide with the
spin of the single particle emitted by the charge.
