We point out that aspects of quantum mechanics can be derived from the
holographic principle, using only a perturbative limit of classical general
relativity. In flat space, the covariant entropy bound reduces to the
Bekenstein bound. The latter does not contain Newton's constant and cannot
operate via gravitational backreaction. Instead, it is protected by - and in
this sense, predicts - the Heisenberg uncertainty principle.Comment: 11 pages, 3 figures; v2: minor correction