Abstract
In quantum mechanics, time plays a role unlike any other observable. We find that measuring whether an event happened, and measuring when an event happened are fundamentally different - the two measurements do not correspond to compatible observables and interfere with each other. We also propose a basic limitation on measurements of the arrival time of a free particle given by
where 
is the particle's
kinetic energy. The temporal order
of events is also an ambiguous concept in quantum mechanics. It is not
always possible to determine whether one event lies in the future or past
of another event. One
cannot measure whether one particle arrives to a particular location before or
after another particle if they arrive within a time of 
of each
other, where 
is the total kinetic energy of the two particles.
These new inaccuracy limitations are dynamical in nature, and fundamentally
different from the Heisenberg uncertainty relations. They refer to individual
measurements of a single quantity. It is hoped that by understanding the role
of time in quantum mechanics, we may gain new insight into the role of time
in a quantum theory of gravity.
