Re: 2 million teachers in 2007!

[John Denker <jsd@MONMOUTH.COM>]

Hi --

At 01:07 AM 8/17/99 -0400, Stefan Jeglinski asked:
> 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.  Clearly it is not a
freely-falling frame.

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.

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.

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;  my laboratory is being accelerated skyward by huge
forces that the earth's crust applies to the foundations (thereby
cancelling the acceleration due to gravity).

Note that in GR, "unaccelerated" is not synonymous with "freely falling".
Consider two spaceships moving along the same orbital path in opposite
directions.  Each is freely falling, but they are forever accelerating
toward each other.

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.

> 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.


> 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.

> 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.

OK?

Cheers --- jsd