Although I see evidence this morning that some still don't fully
appreciate the physical import of the principle of equivalence (POE), I
think this thread has been pretty much settled. I had to leave for the
weekend just after reading David Bowman's characteristically thorough and
masterful summary and, since I've seen no comment on it yet, I wanted to
acknowledge it and take one last shot at summarizing the issues myself.
The POE says that *all* local gravitational fields are, in some sense,
"fictitious." This is not to say that they are not useful. They are
*very* useful but should be understood to lie in the same conceptual
category as centrifugal force--another useful concept.
The POE says that *all* local gravitational fields are the result of
reference frame acceleration with respect to local inertial (free fall)
frames. For instance, it is *not* the gravitational mass of the Earth
that produces the "observed" 9.8 N/kg, downward gravitational field near
its surface. Rather, it is the fact that contact with it's surface
causes us and most everything we see to accelerate at 9.8 m/s^2, upward
relative to the local inertial frames. One can *never* "feel" a local
gravitational force because such forces do not exist. If anything, it is
probably best to say that one "experiences the effects of acceleration."
(Before I am misread, allow me to say that I'm not advocating taking this
position in introductory courses; I'm simply telling "the truth." ;-) )
The POE says that, *whenever* we accelerate with respect to local
inertial frames for *any* reason, we "produce" local gravitational
fields. The possible time-dependence of these fields is not problematic.
The only effect of gravitational mass that the POE does not reveal as
"fictitious" is to cause local inertial frames in one place ("local local
inertial frames") to accelerate with respect to local inertial frames in
another place ("distant local inertial frames" ?). Within General
Relativity this effect is modeled as the result of "curvature of
spacetime" and you can get an idea of "how curved" spacetime is in your
vicinity by dividing the acceleration of local inertial frames in one
place with respect to those in another place by the distance between
those two places. This is what is referred to as the "tidal effect"
which, unfortunately, implies that it is merely an interesting subtlety
of gravitation when, in fact, it is the *only* true gravitational effect.
The discussion on this topic prompted me to create an Interactive Physics
module that simulates the motion of two clusters of projectiles near the
surface of the Earth--one cluster at the North Pole and the other at the
Equator. One can look at either cluster 1) from the reference frame of
the Earth in which case one sees the usual parabolic trajectories with
"local downward" curvatures, 2) from the reference frame of one member of
the same cluster in which case all trajectories are straight lines as one
would expect in a local inertial frame, or 3) from the reference frame of
a member of the *other* cluster in which case one again sees parabolic
trajectories, this time with curvatures toward the other cluster. The
simulation graphically shows the difference between a) observing the
behavior of different local inertial frames *from* a "local local
inertial frame" and b) observing the behavior of local inertial frames
from a "distant local inertial frame."
I will eventually post this simulation with the other IP simulations at
my web site. Unfortunately, the web site of my entire college is broken
at the moment due to a destructive "hack attack" and I am now looking for
another, more secure place to hang my web materials.
John
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A. John Mallinckrodt email: mallinckrodt@csupomona.edu
Professor of Physics voice: 909-869-4054
Cal Poly Pomona fax: 909-869-5090
Pomona, CA 91768 office: Building 8, Room 223