Some of the mild confusion in this thread appears to be the result
of not distinguishing between freely falling objects that are near
other massive bodies and those that are not. It might be good to
back up and review the Newtonian worldview and see specifically
how it differs from that of GR.
I hope the list will excuse my extended exposition here and that
at least a few might find it useful.
THE NEWTONIAN WORLDVIEW
To Newton the universe was a Euclidean stage on which events
played out in absolute time. Because his space was also absolute
--one whose properties were independent of the existence of
objects within it--he could imagine the universe devoid of all but
one object (call it an "inertial test body" or ITB) which would
then necessarily travel at some arbitrary, but constant velocity
since it had nothing to interact with--Newton's First Law.
He imagined that repopulating the universe with massive bodies
(MB's) would have negligible effect on the motion of the ITB or
others like it as long as none of the MB's were "nearby." (I will
call this the "deep space" approximation and return to it at the
end.) All such ITB's would necessarily be traveling at constant
velocity relative to each other no matter how far apart they might
be. Furthermore, each possible ITB could be associated with a
specific "inertial frame."
To identify inertial frames near massive objects Newton imagined
universe-filling, but noninteracting rigid lattices attached to
the ITB's. (We should recognize, but it needn't overly concern us
just now, that this critical step is impractical at best.) Under
these assumptions it is simple to show that the acceleration of
any object in the universe is an absolute quantity--one that is
independent of the inertial frame from which it is measured.
(Nevermind that it is not at all obvious how one would determine
that absolute acceleration, in practice.)
Newton's great success was finding a *self-consistent* 1) system
of mechanics and 2) law of gravity that apparently described the
observed motions of both the planets and objects in the lab under
the assumption that the solar system itself was an extended ITB,
i.e., far enough away from other MB's so as to be negligibly
affected by them.
The process went something like this: Newton imagined that our
motion when we stand on the surface of Earth differs negligibly
for a "suitably long period of time" from that of some inertial
frame--that is, that our absolute acceleration is "suitably
small." Then his Second Law and the fact that we do not
accelerate despite a large and very obvious upward force on our
feet required him to postulate an equal but opposite downward
force of very mysterious, but apparently Earth-related origin.
His postulate was further confirmed by the fact that objects that
do not receive support from Earth's surface accelerate--relative
to us and, therefore, *absolutely*--toward Earth. Newton himself,
probably better than most even today, clearly recognized the
mysterious nature of the "gravitational" force that impels them to
do so.
NB: It is *absolutely critical* to note in the above that Newton's
invention of the gravitational force was a direct consequence of
his bold, unsupported assumption that inertial frames could be
extended throughout space based on the motion of the distant, and
ultimately hypothetical ITB's in "deep space" AND his assumption
that any point on the surface of Earth has a negligible
acceleration wrt the ITB's.
Further analysis of the way "freely falling" bodies move revealed
what Newton could only consider a striking coincidence: Self-
consistency required that the gravitational force on an object be
directly proportional to its inertial mass.
Finally, Newton found that he could, again self-consistently,
obtain agreement with Kepler's laws by assuming that the planets
obey the same law of motion and by tailoring a law of gravity that
among other things fell off as the square of the distance between
any two objects. Pleasingly, this falling off of the
gravitational force with distance provided qualitative support for
the initial notion of "deep space" where real bodies could move in
an essentially force free manner emulating the hypothetical ITB's.
"FREELY FALLING" VERSUS "FORCE FREE" MOTION
Although Newton would surely have recognized that there is no
clear boundary to "deep space," he might have been willing to
distinguish between "force free" motion (as approximated by the
deep space ITB's) and "free fall" (which implies the existence of
a nonnegligible gravitational force.) For Newton, the
acceleration of an object was absolute and universal; any object
with a nonnegligible acceleration was simply not "force free". In
practice, the boundary on "deep space" was determined by the level
of your sensitivity to this very problematic absolute
acceleration.
Einstein did away with the need to make such difficult and
arbitrary distinctions by making freefall the *definition* of
force free motion. GR makes life much simpler--at least in this
conceptual regard--by eliminating the need to refer to the motions
of impossibly ideal "deep space" objects and by putting
gravitational forces in the same camp as all other mass-dependent
inertial forces, but at the cost of recognizing that inertial
frames are necessarily local and that acceleration is *not*
absolute.
------------
Well, enough fun for now. My wife is quite certain that
philosophical musings on the nature of gravitation won't build our
basement door.
Later,
John
----------------------------------------------------------
A. John Mallinckrodt http://www.csupomona.edu/~ajm
Professor of Physics mailto:ajm@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223