Re: [Phys-l] Weightless (running around in circles)

[John Mallinckrodt <ajm@csupomona.edu>]

Jeff,

For the most part I agree with what you have written below.  Just a  
couple of points:

1. You compare what you call "the GR model" to the Newtonian model.   
While any modern view of gravity requires a clear appreciation of the  
deep message of the Principle of Equivalence, I hesitate to call the  
world view I have been advocating here "General Relativistic."  No  
understanding of GR is required, nor indeed is it even necessary that  
there BE a relativistic theory of gravity.  We can patch up the  
Newtonian model very nicely with nothing more than the POE.

2.  It is fundamental to the modern view of gravity that inertial  
frames ARE free falling frames and necessarily, therefore,  
"local".*   It follows that the gravitational force in such frames is  
always zero and that properly functioning accelerometers (probably  
better called "antigravimeters"!) transparently reveal whether they  
are moving inertially.  Nevertheless, I wouldn't want to say that  
"the ... acceleration of ... an object [is] its accelerometer  
reading."  Instead I would say that the acceleration of an object is  
frame-dependent.  It is whatever an observer in the vicinity of the  
object measures it to be.  If that measurement doesn't agree with the  
accelerometer reading, then the observer is not in freefall.  The  
measured acceleration minus the accelerometer reading is the local  
gravitational field in the frame of the observer.

* Note:  There is no ambiguity about what it means to construct  
extended reference frames, this notwithstanding the fact that  
inertial frames are local, because space is Euclidean and time is  
absolute in the hybrid, Newtonian + POE world view that I am  
advocating.  (I believe that this world view may be identical to the  
one that emerges from a fully general relativistic treatment with an  
infinite invariant speed.)  One can, for instance, attach a reference  
frame to Earth and extend it to the orbit of the Moon and beyond.  In  
such a reference frame, g vanishes in the vicinity of the center of  
the Earth.  One could also attach a reference frame to a falling  
rock, extend it, and determine that g vanishes in the vicinity of the  
rock.

John

On Nov 26, 2006, at 8:22 AM, Jeffrey Schnick wrote:

> John M., Do you buy the following?
>
> It seems to me that the big differences between the GR model and the
> Newtonian model have to do with what an inertial reference frame is  
> and
> what acceleration is.
>
> A Newtonian inertial reference frame is something that can only be
> imagined.  One way of doing so would be to imagine a non-rotating
> spherically symmetric object with an ideal accelerometer at its  
> center.
> Have it be and remain at a location in space at which the total GM/r^2
> gravitational field from all matter in the universe is and remains  
> zero.
> (To me, establishing that this is the case is the impossible part.)
> While the object is at such a location, as long as the object's
> accelerometer reading is zero, any reference frame in which the object
> is not rotating and the object's r double dot is zero is an inertial
> reference frame.  As viewed from any such reference frame, the
> acceleration of any object is its r double dot, its Newtonian
> acceleration.  The Newtonian acceleration of an object is always
> accompanied by a net force that is directly proportional to the  
> product
> of the mass of the object and the Newtonian acceleration of the  
> object.
> The force could be a GMm/r^2 force.  A net force is occurring when the
> object is interacting with its surroundings.
>
> An Einsteinian inertial reference frame seems to be much simpler.  Our
> non-rotating spherically symmetric object represents an inertial
> reference frame whenever its accelerometer reading is zero.  The GR
> acceleration of such an object would be its accelerometer reading.  A
> net force on this object would be an ongoing interaction with its
> surroundings that is accompanied by a non-zero accelerometer reading.
> There is no GMm/r^2 force because the mere existence of other massive
> objects has no effect on the already-zero accelerometer reading.
>
> In the Newtonian model, the r double dot of an inertial reference  
> frame
> relative to another inertial reference frame is always zero.  Not  
> so in
> GR.  In fact, GR is a way predicting what that r double dot would be.
> In GR with Newtonian language, one can describe the r double dot of an
> object whose accelerometer reading is zero, relative to another object
> whose accelerometer reading is zero, in terms of a pseudo force,  
> and we
> can call that pseudo force a gravitational force, but it is not a GR
> force because it doesn't change any accelerometer readings.
>
> Jeff Schnick

John Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://outlawsofphysics.com>