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

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

Bob Sciamanda said

> Please comment (and be gentle!)

(I do sincerely apologize if I've appeared to be less than gentle in my 
recent posts.  I suspect that, at times, I have.)

But before that he said,

>         ... I just checked some
> writings of Einstein, Gamow, Bondi, and Reichenbach.  They all take
> something like the following viewpoint:
>
> 1) GR abolishes the preferred position of the Newtonian class of inertial
> frames (the "fixed stars" being one) by allowing an observer to transform
> away his (Newtonian) acceleration by taking account of dynamic, covariant
> gravitational fields with identifiable sources (including the distant
> stars). Here we are transforming away acceleration in favor of gravitation.
>
>         Your (more modern?) viewpoint :
>
> 2) The only inertial frame worthy of the name is the local free fall frame.
> The observer in that frame is neither accelerating nor gravitating.
> Departures from that frame are produced by accelerations (relative to
> that frame).  An observer thus accelerating will see kinematical effects
> which will be identical to the effects of a gravitational field, but
> this field is fictitious and has no source beyond his acceleration
> itself. Here we are transforming away gravitation in favor of acceleration.

I stipulate that #2 is a fair representation of what I've been saying.  
I'm not quite sure, on the other hand, how you are reading #1.  With only 
a little clarification, I read it as being completely compatible with #2.  
The final sentences do seem to imply an either/or proposition, but I 
think that putting acceleration and local gravitation on an equal footing 
is the very essence of the principle of equivalence.

You may (understandably) be misreading me as disavowing the role of 
matter with respect to the appearance of local gravitational fields.  I 
do maintain that it is one's acceleration relative to the local inertial 
frames that *determines* the gravitational field instant-by-instant.  But 
you may have noticed that I've not dealt directly with the question of 
what determines the local inertial frames.

In Newtonian mechanics we pin inertial frames on the backs of objects in 
some impossibly ideal "deep space" where they are *unaffected* by 
gravitational influences.  Their motion is as it is because of the 
absence of *any* effect whatsoever from other matter.  Yet, in a universe 
without matter it would be utter nonsense to claim that some motions are 
preferred to others.  After all, what could "motion" possibly mean in 
such a universe?  (Mach, et.al.)

It seems clear, then, that the matter in the universe is somehow 
responsible for singling out the local inertial frames.  But it is *all* 
the matter in the universe--not just the planet you happen to be standing 
on--that does the singling out.  The reason we get away with pretending 
(for that *is* what it is) that the gravitational field we "experience" 
is due only to the earth is the result of three semiremarkable and 
independent facts: 1) The earth is not acted upon by any significant 
external forces. (Just a reminder: gravity is not a force.) 2) Our 
acceleration relative to the center of the earth is negligible. 3) The 
earth moves through a region of space with a negligible background tidal 
effect. Because of 1) the center of the earth is a local inertial frame.  
Because of 2) the surface of the earth *would* also be a local inertial 
frame *if* the tidal effect between the center of the earth and the 
surface were negligible.  Because of 3) the *only* significant 
contributor to the tidal effect between the center of the earth and the 
surface is the earth itself.  If any *one* of these three facts were 
violated (e.g., a giant hand pushed--giantly--on the south pole, the 
earth's rotational period decreased to a couple of hours, or the earth 
orbited just outside the event horizon of a not too enormous black hole), 
then there would be no clear correlation between the mass and size of the 
earth and the apparent gravitational field at its surface.  Indeed, the 
locally observed gravitational field would take on very different values 
at different places on the surface and at different times.  We are 
already familiar with a weak version of the above due to the not really 
so negligible violation of condition 2.

So yes, the matter matters, but I think it is fair to read GR (a still 
not-so-well tested theory) fundamentally as being a prescription for how 
matter determines local inertial frames.  After *that* is done, all we 
need is equivalence (a far simpler and less controversial principle) to 
determine the gravitational field anyone will "observe."

Gentle enough?

John
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