Re: operationally inertial frames

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Wed, 13 Oct 1999, John Denker wrote:

> At 06:15 PM 10/12/99 -0800, John Mallinckrodt wrote:
> 1>
> 1>For me, it is because there is no satisfactory operational way to
> 1>determine whether or not you are in a so-called "inertial frame."
>
> 2> I feel
> 2>liberated by the modern viewpoint which holds that *all* frames are
> 2>equivalent and that any inertial force is a gravitational force.
>
> Passage <2> expresses the corret physics.  I cannot understand passage <1>;
> it seems totally inconsistent with the correct physics.
>
> ... the literature contains two inconsistent definitions of "inertial frame".
>   a) The high-school level literature typically deals with what might be
> called "Newtonian inertial frames", such as frames attached to the earth's
> surface.
>   b) The modern physics literature (in particular the general relativity
> literature) typically reserves the term "inertial frame" to refer to
> "freely falling frames".
>
> In forums such as this list, where there are people with wildly divergent
> backgrounds and interests, it is best to be ultra-explicit.  I will use the
> term "Newtonian frame" for item (a) and "freely-falling frame" for item (b).

We are in agreement.  I had hoped that my phrase "so callled 'inertial
frame'" would be interpreted as your "Newtonian frame."  You are also
right about the need to be ultra explicit.  (BTW, in the interest of ultra
explicitness, I would prefer "Newtonian inertial frame.")  Looking back
over this thread, I suspect that at least some of our apparent
disagreements were actually failed communications.

> The operational procedure for determining whether you are in an inertial
> frame is to do an experiment to detect non-inertial effects.  If you get a
> null result, you are in an inertial frame, within your chosen level of
> accuracy.

Hmm.  I think you mean to say "an experiment to detect inertial forces"
don't you?

> Example 1 (Newtonian):  it is easy to show that the earth's surface is not
> quite a Newtonian frame.  Just set up a Foucault pendulum and watch it for
> a while.  OTOH the Foucault effect and other nonidealities are small, so
> for most purposes it is an appropriate approximation to consider the
> earth's surface to be a Newtonian frame.

Well... It is certainly possible in some cases to show that you are not in
a Newtonian inertial frame, but it is *not* possible to show that you are
even approximately *in* one.  It can be an "appropriate approximation" to
consider the earth's surface a Newtonian inertial frame even if it is
*nothing at all* like one.

Consider this: To establish that a reference frame is a Newtonian inertial
frame, you need to demonstrate that it is not accelerating with respect to
other Newtonian inertial frames, e.g., those that are free floating in
deep space.  This is often stated as "not accelerating with respect to the
distant stars."  But there is no way to perform such a demonstration for
the simple reason that, as we now know, free floating frames in deep space
and distant stars all generally accelerate with respect to each other!
Nevertheless, if the earth and all of its occupants were accelerated in
some direction at an arbitrarily large rate, say 1000 g, we'd have *no*
local way of detecting that fact and we could treat the earth's surface as
a Newtonian inertial frame anyway.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm