In the 1950s, Landau, Pomeranchuk, acid Migdal (LPM) predicted that th
e cross section for bremsstrahlung from highly relativistic particles
in dense media would be suppressed due to interference between amplitu
des of nearby interactions. We have measured the production rates of 5
to 500 MeV photons from 8 and 25 GeV electrons traversing thin gold a
nd carbon targets. We observe, to within 5% accuracy, suppression at t
he level predicted by Migdal. For extremely thin targets, we observe '
'edge effects'' where the LPM suppression is reduced near the edges of
the targets. We also point out the imprecise foundation of the LPM th
eory.