Here and now

"Here and now" is the (observer-dependent and hence subjective) choice of a space-time reference point singled out by the place where and the time when the choice is made. The time and place where an observer refers to here and now define the point in space-time implied. If several observers (or the same observer at different times) refer to here and now they refer to different points in space-time.

The precise physical meaning of "here" and "now" is the following: A sufficiently large (and hence to a sufficient approximation classical) observer may regard its classical trajectory as defining "here", a particular point on it (namely the one at which the observer makes its choice) as the "here and now", and then consistently regard "now" to be the spacelike sheet defined at least locally by Riemann normal coordinates orthogonal to the trajectory tangent.

Note that the notion of "here and now" determines the space-time position only within a spatial uncertainty of the order of the size of the speaker or writer, and a temporal uncertainty of the order of the time it takes to say or write the word.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ