Natural Science Forum / Physics / Relativity / March 2005

Not accelerating except in gravity.

Fred Chen:

  In general relativity, there are no inertial frames, so inertial
frames only exist to the extent that such an approximation is useful.
Such approximations are often useful and hold very well for quite
large accelerations if one treats an accelerated object as instantan-
eously inertial at every point along its world line.

I like the definition by Landau in Mechanics.  It is a frame that is
homogeneous in space and time an isotropic in space.  That puts the emphasis
where I believe it really belongs - on the symmetry properties of such a
frame.

Thanks
Bill

I agree with you 100% Fred on that last thought. Clearly, there are no true
inertial frames actually found in Nature... it is a hypothetical concept
only, an imaginary vantage which is not acted upon by *any* external forces
whatsoever. Yet gravity is everywhere, so alas.

But because the math of Relativity is so mild in the less extreme venues, we
do wind up using approximations and treating them as if they deviate
negligibly from actual inertial frames.

As with most statements attributed to Mach, that is too nebulous for any
real use. In particular, there _are_ no "fixed stars" (a phrase commonly
used in this context). And the "distant stars" do not form a "reference
system" in any recognizable sense (they move with respect to each
other). Moreover, the visible "distant stars" are mostly in our own
galaxy, which is known to be rotating....

Moreover, since 1915 or so we have a clear and obvious way out of your
dilemma -- use GR, in which "inertial reference frame" is reduced to
only local usage and meaning. It is quite clear that there is no such
thing as an "inertial frame which covers the universe", and the approach
of GR fits well with such observations.

This is, of course, an APPROXIMATION. For instance, in most tabletop
optical experiments performed in a laboratory on earth, one can analyze
the system using SR, because during the transit time of the light beams
the non-inertial motions of the lab are negligible. [some systems, like
fiber-optic gyroscopes, must be analyzed taking into account the
rotation of the earth.]

Yes. And if they are at rest on the surface they are also accelerating
upward relative to any locally-inertial frame (in the GR sense). But
still, for many experiments (e.g. tabletop optics, high-energy particle
collisions, ...) the "lab frame" is so accurately inertial that using SR
is no problem.

In the light of GR this is the best one can hope for. Live with it.
Nature has no need for human "reassurance"....

Tom Roberts    tjoberts@lucent.com

Well, it's both. There's a theoretical notion of inertial frame which is
precise and exact, and an empirical notion which is imprecise and
provisional. The theory is supposed to approximate the reality, but often it
feels like it's the other way around...

-- Ben