In conventional quantum physics, space and time coordinates commute and
spacetime is described by its commutative algebra of functions.But there
are now a number of models suggested by noncommutative geometry, string
physics and quantum gravity where space and time do not commute. There is
an uncertainty relation connecting space and time coordinates which
precludes observations at an instant of time. This has striking
consequences such as loss of causality, and violations of CPT and
spin-statistics theorems. Even the formulation of quantum physics needs
new ideas from operator algebras and their positive maps.
 This talk will review these emergent ideas at an elementary level
hopefully accessible to both physicists and mathematicians.