Questions of Infinity
Questions of Infinity include:
: Is it infinite? There appears to be only a finite past but an infinite possible future.
: If it is infinite, how did infinitely distance places know how to synchronize their starting time with us (the horizon problem)
: Do they contain infinite information? Algorithmic information theory tells us a field contains only the amount needed to specify it. Thus a gravitation field is defined through all space for a large mass M
and a test particle m
as exerting a force F = GMm/r2
. But there is nothing substantial at an arbitrary point r
. There is information there, in the form of knowledge about the gravitational force on m
is at that point. This is called "action-at-a-distance," but it is also "knowledge-at-a-distance."