Re: Centrifugal force

[Leigh Palmer <palmer@sfu.ca>]

> At 7:59 PM -0700 4/30/98, Leigh Palmer wrote:
> > Think about Donald's hovering rocket ship (a nice improvement on
> > Einstein's elevator). I don't have the quote around, so I'll make
> > up my own. A rocket ship hovers one meter above its launch pad.
> > In the laboratory within an astronaut performs physical experiments
> > (with all manner of apparatus, lasers etc.). At one instant in time
> > God picks up Her fungo bat and decides to improve the situation in
> > the universe by removing the Earth with the speed of light to the
> > most remote place possible. The feat is accomplished in a direction
> > which is horizontal at the pad. The astronaut feels, perhaps, a
> > slight bump as the solar system is cleansed, but he continues with
> > his experiments and notices no difference whatever in the results
> > he obtains with those obtained in the same experiments before. The
> > rocket ship lab is and always was the same sort of frame of
> > reference, clearly not an inertial one.
> >
> > Leigh
>
> GREAT thought experiment!!!! Thanx all!

Thanks are due only to Donald Simanek; I just jazzed it up a bit.

> Next question. Let's ignore the 'slight bump' but keep in mind that the
> rocket DOES have a finite size. If our experiments are accurate enough can
> we not measure that two falling objects in the rocket will move closer to
> each other because of the non-uniformity of a 'real' gravitational field,
> than they would when the acceleration is 'caused' by the rocket blast?
>
> I'm familiar with the word 'local' used to describe the principle of
> equivalence and GR, but is there a fundemental arguement that forbids our
> experimentally distinguishing between the divergent gravitational field and
> the uniform acceleration of the rocket??

Not at all; that's certainly part of physics. It's not a system we've
been discussing, however. (I think you mean a convergent field, by
the way. That is to say, a field which converges in the laboratory.
The (mathematical) divergence of the field is zero everywhere, of
course. We are talking about an empty laboratory. You must be careful
when you use the word "divergence" in a scientific context. Even the
word "divergent" may connote a quantity with nonzero divergence.)

Alternatively, if one wishes to make the Earth's gravitational field
uniform, that can easily be done in principle by shimming - placing
piles of Earth beneath the rocket to homogenize the gravitational
field. Would that make the gravitational field somehow less real?

It is easy to make a divergent gravitational field, or one that mimics
centrifugal force in the laboratory. Superposition is an elegant tool
to use in crafting such creatures. The gravitational field on the axis
of a massive uniform ring has both convergent and "divergent" domains
along its axis.

Here is a nice problem for you to consider. It is possible to ascribe
an energy density to electric and magnetic fields. This can also be
done for the gravitational field. What is the gravitational field
energy density at Earth's surface? Please solve the problem starting
from first principles, namely Newton's law of universal gravitation.

Leigh