Re: POE summary (was Re: Work/Energy theorem?)

["Paul Camp" <pjcamp@coastal.edu>]

> Here I am willing to be a little more persnickety, but it may just be 
> semantics.  It sounds a *little* like you agree with the idea others have 
> expressed that there is something fundamentally different about a 
> gravitational field and an acceleration with respect to the local 
> inertial frames.  

No, not really. But it seemed to me that some of the confusion in the 
ensuing discussion revolved around attempts to evade the locality 
condition. 

> I have acknowledged the role of distant matter in 
> determining the *true* (tidal) gravitational effect which I see as 
> essentially equivalent to determining local inertial frames throughout 
> space,

This sounds like Mach's Principle, which is only imperfectly embedded 
in General Relativity. See Misner, Thorne and Wheeler for a 
discussion. You can determine a local inertial frame without 
reference to distant matter. It is a frame in which the first 
derivative of the metric vanishes (a mathematical statement of the 
equivalence principle). The gravitational field tensor depends on 
the second derivative.

> but I maintain that the appearance of a gravitational field (i.e., 
> a force per unit mass, not a curvature tensor) is *always* a local 
> phenomenon and simply an artifact of one's acceleration wrt the local 
> inertial frames.  

This, then, is also where some semantic confusion lies. The 
gravitational field in modern terms *is* a curvature tensor, not a 
force per unit mass. I suppose this is the point where I departed 
from understanding what you were getting at since that really 
involves nongravitational interactions as well. If gravity were the 
only factor, you would not have an acceleration with respect to your 
local inertial frame.

> I maintain that it makes no more sense to talk about 
> global gravitational fields then it does to talk about global inertial 
> frames. Yes, you can always observe freely falling objects at distant 
> locations (whether you are on the surface of the earth or in a 
> decelerating train), notice how they are accelerating, and infer the 
> distant gravitational fields.  But the fields you so infer are particular 
> to *you*; they depend on *your* acceleration wrt *your* local inertial 
> frames.  All you have really done is to determine the local gravitational 
> field that an observer *at* that location but moving without acceleration 
> with respect to *you* would observe.

Yes. And that is all the gravitational field there is. All 
gravitational effects are tidal and manifest themselves only by means 
of nonlocal experiments such as the one you describe here. This 
deviation of geodesics gives information about the curvature of 
spacetime which completely determines the gravitational field, at 
least so long as both objects are freely falling. If they are not, 
then we are talking about other forces besides gravity and it doesn't 
make sense to me to include them in a definition of "gravitational 
field."


> In any event, the central point of this thread is (or at least was) the 
> answer to this question:  Do you claim (as it sounds a little like you do 
> in the above) that a person standing on the surface of the earth sees his 
> or her gravitational field for "better" or *in any way whatsoever* 
> fundamentally *different* reasons than a person in a decelerating train?  
> Regardless of any of the semantically-challenged prose above, I'll bet we 
> agree here.
We do.

 
Paul J. Camp                   "The Beauty of the Universe
Assistant Professor of Physics  consists not only of unity
Coastal Carolina University     in variety but also of 
Conway, SC   29528              variety in unity.
pjcamp@coastal.edu                    --Umberto Eco
pjcamp@postoffice.worldnet.att.net    The Name of the Rose
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