Re: Centrifugal force

["A. R. Marlow" <marlow@loyno.edu>]

On Sat, 2 May 1998, Leigh Palmer wrote:
> ...
> As I pointed out in another message it is quite simple to produce a
> gravitational field which either converges or diverges, or else is
> homogeneous to any hypothetical degree one specifies, over a volume
> as large as one wishes, within reason. ...

This is quite true, and to produce such gravitational fields you need to
produce a *nonzero Riemann curvature tensor* (even for a *uniform* nonzero
gravitational field).   Flat spacetime, i. e., zero Riemann curvature, 
gives only a zero gravitational field.  All this was pointed out in the
previous lengthy discussion, with reference to the AJP article where such
fields and Riemann curvatures were constructed.  

> ...
> The point of Einstein's principle of equivalence is that within the
> region over which the field can be considered to be uniform, there
> is *no observable difference* between phenomena which might be
> attributed to a gravitational force originating outside the frame
> and phenomena attributable to an inertial force due to a uniform
> acceleration of the frame. ...

A nonzero curvature tensor can always be distinguished from the effects of
uniform acceleration of a frame.  The latter can be transformed away by
coordinate changes, the former cannot.  As Synge has noted, the principle
of equivalence was a marvelous midwife at the birth of general relativity,
showing Einstein how special relativity had to be modified to accommodate
gravitation.  The principle, applied in the context of a false theory  --
flat special relativistic spacetime + Newtonian gravitational force  --
showed how to distinguish between true gravitational effects and effects
that were merely frame effects, and led to the modern theory of
gravitation as curvature of spacetime.  The principle as stated above,
however, is *not* a principle of the finished theory, in which even a
uniform nonzero gravitational field must be identified with nonzero
Riemann curvature, which cannot be equivalent to any acceleration of
frames.  To invoke the principle in the context of the modern theory of
gravitation is to confuse the previous flat spacetime+Newton with the
present theory.        

> ...
> A difference, to be a difference, must make a difference. (I've
> also forgotten the attribution for this sage observation.)
> ...

Whatever the attribution, it is certainly sage.  The difference the
Riemann curvature makes has been pointed out twice now.  Is there a flaw
in the argument?  If not, then it certainly should make a difference.
   

A. R. Marlow                          E-MAIL:  marlow@loyno.edu
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