Physical significance of Planck length

Abstract

The significance of Planck length in a quantum gravity model is investigated by concentrating on the conformal degree of freedom. It is shown that Planck length is a lower bound to physical proper length in any space-time. It is impossible to construct an apparatus which will measure length scales smaller than Planck length. These effects exist even in flat space-time because of vacuum fluctuations of gravity. It is shown that these fluctuations lead to a high energy cut-off in flat space field theories, thereby removing the divergence problem. The one-loop corrections to a self interacting scalar field is computed and shown to be finite.