  We show how unobservable causal loops arise from quantum mechanics, and can
explain quantum measurement consistently with macroscopic realism. We analyze a
measurement $\hat{x}$ on a system prepared in a superposition of eigenstates
$|x_{j}\rangle$ where the measurement is modeled by amplification. We prove an
equivalence between the positive phase-space distribution $Q(x,p,t)$, and
simultaneous backward and forward-propagating stochastic trajectories for
amplitudes $x$ and $p$. The sampling for the amplified variable $x$ is
specified by a future boundary condition determined by the measurement setting,
the backward and forward trajectories being linked at the initial-time boundary
to form a loop. We confirm that the joint densities for $x(t)$ and $p(t)$ yield
$Q(x,p,t)$, thus demonstrating causal consistency and Born's rule. A feature is
hidden vacuum noise associated with an eigenstate. Unlike the eigenvalue
$x_{j}$, this noise is not amplified, the fluctuations originating from future
boundary conditions. For macroscopic superpositions of $|x_{j}\rangle$, we show
consistency with macroscopic realism: the outcome for $\hat{x}$ can be
considered a real property at the time $t_{0}$ prior to measurement
(independent of future events). We deduce a hybrid causal structure involving
causal relations for amplified variables, along with hidden causal loops for
unamplified quantities, demonstrating that causal loops do not imply
(observable) retrocausality. Further, we evaluate $Q_{j}(x,p,0)$ for the
trajectories conditioned on the outcome $x_{j}$. The ``state'' defined by this
function cannot be a quantum state, the uncertainties for $\hat{x}$ and
$\hat{p}$ being too small. However, $Q_{j}(x,p,0)$ approaches that of
$|x_{j}\rangle$ for a macroscopic superposition. Our results provide a
framework for study of Einstein-Podolsky-Rosen and Bell correlations.
