A high-intensity, low-emittance atomic muonium (M
=\mu^+ + e^-=μ++e−)
beam is being developed, which would enable improving the precision of
M spectroscopy measurements, and may allow a direct observation of the
M gravitational interaction. Measuring the free fall of M atoms
would be the first test of the weak equivalence principle using
elementary antimatter (\mu^+μ+)
and a purely leptonic system. Such an experiment relies on the high
intensity, continuous muon beams available at the Paul Scherrer
Institute (PSI, Switzerland), and a proposed novel M source. In this
paper, the theoretical motivation and principles of this experiment are
described.