  This paper proposes an explanation for the Pioneer anomaly: an unexplained
Sunward acceleration of 8.74 +/- 1.33 x 10^-10 m s^-2 seen in the behaviour of
the Pioneer probes. Two hypotheses are made: (1) Inertia is a reaction to Unruh
radiation and (2) this reaction is weaker for low accelerations because some
wavelengths in the Unruh spectrum do not fit within a limiting scale (twice the
Hubble distance) and are disallowed: a process similar to the Casimir effect.
When these ideas are used to model the Pioneer crafts' trajectories there is a
slight reduction in their inertial mass, causing an anomalous Sunward
acceleration of 6.9 +/- 3.5 x 10^-10 m s^-2 which agrees within error bars with
the observed Pioneer anomaly beyond 10 AU from the Sun. This new scheme is
appealingly simple and does not require adjustable parameters. However, it also
predicts an anomaly within 10 AU of the Sun, which has not been observed.
Various observational tests for the idea are proposed.
