Re: [Phys-l] definition of gravity

[John Denker <jsd@av8n.com>]

On 11/08/2011 12:37 PM, Bill Nettles wrote:
> In SR (and GR?) we make a big deal out of the mass being invariant.

Yes.  For good reason.

> Why can't we _define_ gravity as being Gm/r2 and let accelerating
> reference frames modify this?

Well, which is it?  Are you recommending that we define
"gravity" as GM/r^2 ... or is the definition "modified" 
by the acceleration of the frame?

In modern (post-1915) physics, the "modification" is a 
complete replacement, in the sense that if you know the 
acceleration of the frame you know the local gravitational
acceleration (g).  This is the definition that is used in 
real, practical applications, all day every day.

As for the magnitude |g|, for some applications it is OK
to approximate it by the Newtonian GM/r^2.  

Meanwhile, in temperate latitudes, the /direction/ of 
the g vector differs quite noticeably from the Newtonian
prediction.  Let's be clear: the real, practical g does 
not point toward the center of the earth.  This is not
some obscure hyper-theoretical result.  If you build a
tall building aligned with its up/down axis aligned with
the direction toward the center of the earth, people 
will think you are crazy.  If you build a swimming pool
with its horizontal directions perpendicular to the
direction toward the center of the earth, people will
think you are crazy.  The water in the pool has its own 
notion of horizontal, in accordance with the laws of 
physics, which does not agree with the "center of the 
earth" notion.

I guarantee you that every architect on earth defines
the direction and magnitude of g in terms of the
acceleration of the frame, as measured relative to
freely-falling objects.  This is the practical definition
as well as the modern-physics definition.

If you want to change this to something else, you will 
need a very specific counterproposal, and a very strong 
argument in favor of the change.