Re: is free-fall an inertial frame?

[Stefan Jeglinski <jeglin@4PI.COM>]

> > is free-fall an inertial frame?
>
> Yes, no, and maybe.
>
> We have here a nasty inconsistency between definitions.
>
> 1) Many introductory texts use a Newtonian point of view.  They consider
> the earth's surface to be an unaccelerated reference frame.  They further
> designate it as an inertial reference frame.


True, the introductory texts are not as careful, but I try to turn to
texts like Goldstein and Marion to seek clarification. Both do a good
job of a) detailing motion in a non-inertial frame and b) not
answering my question. But I am beginning to gather that this is
because something of what I am saying is ill-posed. My confusion
first arose when I then compared the Goldstein/Marion to the
treatment of inertial frames in Taylor and Wheeler's SpaceTime
Physics.


> 1a) In the "rigid Newtonian" viewpoint the only allowed reference frames
> are those attached to the earth, or ones that differ therefrom by a
> constant velocity.

Here is the first part of my problem. I see no a a priori reason to
neglect free-fall, even in the rigid Newtonian view. Is there a
concise statement of why free-fall should not be included in the
'classical' discussion of frames of reference? My problem from a
teaching standpoint is that the introductory texts go on to talk a
lot about free-fall in describing mechanics and presenting word
problems. Not discussing free-fall w.r.t. inertial or non-inertial
frames seems a glaring oversight.


> 1b) In the "enhanced Newtonian" viewpoint they might allow the term
> "inertial" to cover freely-falling frames also, but they typically don't
> even consider this case.


Exactly.


> 2) Things change when we advance to the General Relativity view.  In this
> context, the label "inertial" typically applies *only* to freely-falling
> frames.  The earth's surface is *not* considered an unaccelerated frame or
> an inertial frame;

Even in an approximate sense? The Goldsteins and Marions present
discussion that considering the earth to be an inertial frame is an
approximation only as good to the degree that the other
[pseudo]forces can be ignored. IOW, depending on your calculational
need, the earth can be considered an approximate inertial frame. Is
this not true in GR?


> My recommendation is to avoid the term "inertial" since it has these
> conflicting definitions.  I use the term "freely-falling" when that's what
> I mean (i.e. in GR contexts).  I use the term "Newtonian" to describe
> frames attached to the earth, or differing therefrom by a constant
> velocity.  I'm open to suggestions for better terminology.


As am I. Part of this is a mid-life crisis about whether I think
Newton's Laws are worded very well. From a teaching standpoint, I
have found that Newton's 1st (and 3rd) Laws are responsible for as
many wrongs answers from physics learners as right answers (maybe
more!). IOW, they can get you in as much trouble as they get you out
of.


> >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."
>
> That's fine, but it is subject to two different interpretations, depending
> on which definition of "inertial" you take.  In the Newtonian view, gravity
> produces "known" forces;  in the GR view it does not.


I sense this as a crucial distinction. But let me try to quote a
notion that keeps revolving in my head and drives me crazy: "when I'm
in free-fall, I can't feel that it is gravity causing it; to see that
gravity causes the free-fall, I have to stand outside the earth, in
an inertial frame. But free-fall is an inertial frame to begin with;
why then do I need to stand outside in another inertial frame to see
gravity as a "known" force?" I don't seem to have this conflict with
any other force. I seem to be able to identify "pushes" and "pulls"
and friction and drag (etc) and electrostatic force as known forces,
and coriolis and centrifugal forces (etc) as pseudo forces due to
accelerated or rotating frames-of-reference. But gravity itself...


> >So, by all accounts, these should suggest that free-fall is in
> >inertial frame.
>
> Right.  Depending on which definition you take, free-fall is either a
> proper subset of the inertial frames, or the defining property thereof.
>
> >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"?
>
> That statement is inconsistent with the GR viewpoint.  It announces that
> the book is taking the "rigid Newtonian" viewpoint.

Which takes me back to my question of what a priori reason exists to
exclude free-fall from the rigid Newtonian discussion of frames of
reference. I feel like you're getting around to saying that there is
something particularly instructive (I hesitate to use the word
"special") about free-fall. It appears to cause this confusion but
also provides a bridge from a Newtonian view to a GR view.


> >Free fall is clearly an accelerating frame,
>
> Not necessarily.  It accelerates relative to the earth, and it accelerates
> relative to other far-away frames, but it doesn't accelerate relative to
> other free-falling frames that are moving past its location.

Another crucial distinction? I understand this one, but I have to
think about it's ramifications...

> OK?


Thanks for humoring me.


Stefan Jeglinski