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is free-fall an inertial frame?



A question that's been bugging me for a while...

I argue yes for the following reasons, and then pose the $10,000 question.

1. Newton's 1st Law is essentially a means of defining an inertial
frame. It has a number of various wordings, similar to "any object at
rest tends to stay at rest, and any object in motion tends to stay in
that motion (straight line assumed), unless acted on by an outside
force."

Personal note: I've always been dissatisfied with this description,
and one of my old committee members and I came up with this ditty that
I like better but which I admit also suffers from lack of rigor: "if you
see (experience) a force for which there is no known acceleration, or
an acceleration for which there is no known force, you are in a
noninertial frame."

2. An observer in free fall will note that Newton's first law in his
locality appears to hold. A local accelerometer registers nothing, as
all its parts are in the same free fall, as are all objects around
him or her. And it appears obvious that if one propels an object to
the side (perpendicular to the free fall vector), one notes an
"inertial" behavior: the object continues in an apparent straight
line at constant velocity as far as the observer is concerned.
Propelling an object in the direction of the free fall yields a
similar result, although not quite as obvious.

So, by all accounts, these should suggest that free-fall is in
inertial frame. For simplicity I am assuming free fall with no air
resistance. I also note that since there are no absolute inertial
reference frames, any inertial frame definition is not complete
without a specification of the limits of measurement of distance and
time (and hence acceleration) in that frame. An inertial frame is
only inertial to the extent that measurements cannot detect its
non-inertial nature. For example, the earth's surface is an inertial
frame in *some* approximation (one in which coriolis effects are not
noticeable, for example), just as a reference frame based on the
position of distant stars is also an approximation (albeit a better
one). Likewise, a spaceship (for example) in free fall whose
dimensions are small enough such that all particles in that spaceship
experience the same free fall to within a specified measurement, is
also considered an inertial frame. The spirit of my question is such
that these points are not objections.

So my problem is: if everyone would agree with this, why does every
mechanics book I read state something to the effect of "an inertial
frame is a non-accelerated (constant velocity) frame"? Free fall is
clearly an accelerating frame, but it appears to be inertial (again,
within certain limits which do not change the concept but make it
more rigorous). Why do the mechanics books seem to ignore this? It
would seem to me that saying "an inertial frame is a non-accelerated
(constant velocity) frame" is very misleading because of this one
example.

Sorry that the setup was no long compared to the question, but it is
just reflecting the way I am trying to carefully step through this
minefield. Looking for comments and clarifications. Fire away!



Stefan Jeglinski