Re: summary of elevator equivalence

[John Denker <jsd@MONMOUTH.COM>]

At 01:48 AM 10/17/99 -0400, Raacc@aol.com wrote:
> As a fixed observer on the earth, can I determine
> whether a force acting on a mass
> in an elevator (relative acceleration
> less than g) is gravitational or not?
> I have all conventional measurements at my disposal.

Einstein's principle of equivalence states:
           At any particular point in spacetime,                 (1)
           a gravitational field is indistinguishable from       (2)
           an acceleration of the reference frame.

The conclusion (2) is not valid without the proviso (1).

So, to answer the question at hand......

A) If "all conventional measurements" is meant to include multipoint
measurements such as observing the orbit of the earth's moon,
Jupiter's moons, et cetera, then you can definitely determine the
earth's gravitational field to several significant figures.  You can
communicate this to your buddy in the elevator.  No problem.

B) OTOH if "fixed observer" means restricting yourself to a smallish
region of spacetime (a few cubic meters and a few seconds) with no
looking outside, then you will only be able to observe the acceleration
of dropped objects (which I will call g_o).  You will be able to write
abstract equations of the form
        g_o = g_g + g_x
where g_g is the acceleration due to genuine gravitational GMm/r^2
effects, and g_x represents all other types of acceleration...

... but (!) you will have an exceedingly hard time ascertaining the
separate contributions g_g or g_x (still assuming no looking outside).

B.2) Your buddy in the elevator will have a slightly different value
for g_o and g_x (and maybe even a very slightly different value for
g_g) but he will not be able to separate g_g from g_x either (again
assuming his measurements are confined to a smallish region of
spacetime).

B.3) The two of you working together will be able to do somewhat
better than either of you separately.  In particular, if the elevator
is moderately distant from your lab, you could use surveying
techniques to ascertain that his "down" direction is different from
your "down" direction, thereby putting some kind of bounds on the
values of g_g and g_x.  This is a multipoint measurement so the
equivalence principle does not forbid it.

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com