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

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Fri, 11 Apr 1997, Paul Camp wrote:

> There is an important point about the principle of equivalence that
> is being missed in this discussion -- it only applies *locally*. You
> don't get to make global statements or make measurements of things
> that are not located at the same place as you. This includes sources
> of gravitational fields. They are perforce not where you are and so
> you don't get to talk about them in a local context.

No major argument here (except for the bit about "sources of 
gravitational fields."  See below.)  I thought I had made this point.

> The equivalence principle does not say that gravitational fields and
> uniform accelerations are the same thing. It does say that *locally*
> they cannot be distinguished. *Locally* the only thing you can
> measure is your acceleration and you cannot tell what the source of
> it is.

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.  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, 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.  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.

BTW, quite contrary to your last statement above, I think you can almost
*always* determine the "source" of your acceleration (and, therefore, of
your local gravitational field. ;-) ) It will likely be in "direct
physical contact" with you--e.g., the ground!

> Yes, you can formally replace the uniform acceleration of a train
> with a uniform gravitational field *locally* but that does not mean
> that it *is* a uniform gravitational field, simply that it is
> equivalent to one. If you want to look for sources, you must do a
> nonlocal experiment and then you can tell the difference between the
> two.

I'm not sure what you are getting at when you write of the "uniform 
acceleration of a train."  I can imagine it meaning 1) that every 
location on the train has the same acceleration wrt the surface of the 
earth or 2) that it is constant in time.  But isn't the instantaneous 
acceleration of the observer all that matters?  Similarly what sense am I 
to make of the phrase, "uniform gravitational field *locally*"?  

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.

John
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