The concept of ''Now''
Time is passing. This means that what is ''now'' in our subjective experience changes. But there is no concept of ''now'' in physics.
Classical nonrelativistic mechanics does not know the concept of now. One declares some time to be ''now'' - but which time one declares to be ''now'' is completely subjective (i.e., in different situations it will be declared differently). Similarly, one declares some position to be ''here'', but which position you declare to be ''here'' is completely subjective, in the same sense.
Since different people assign at different times a different meaning
to the time called ''now'' and the position called ''here'', these words
have - from an objective point of view - simply the meaning of a
variable denoting time and position, respectively.
The precise extent of this subjectivity is described in my article '' Here and now''.
Classical relativistic mechanics does not know the concept of now,
either, but things change a little: Here one declares some event
(= spacetime point) to be ''here and now'' - again, which event one
declares to be ''here and now'' is completely subjective.
Nonrelativistic quantum mechanics treats time completely differently from space (time is a parameter, space coordinates are operators), and introduces stochastic elements into the dynamics. but with respect to ''here'' and ''now'', the situation is identical with that in the classical nonrelativistic case.
Relativistic quantum mechanics restores the treatment of space and time on equal footing (space and time coordinates are parameters). But with respect to ''here and now'', the situation is identical with that in the classical relativistic case.
Once one has chosen ''here'' and ''now'', respectively ''here and now'', it serves as origin of the tangent hyperplane, in which localized, flat physics can be done, reflecting faithfully what happens in a neigborhood of the spacetime point. This is the domain of relativistic quantum field theory.
Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ