Re: Falling Balls, Revisited


Spoonfed wrote:
> Ken S. Tucker wrote:
> > Spoonfed wrote:
> > > Ken S. Tucker wrote:
> > >
> > > > Then the balls will vertically separate as they fall,
> > > >
> > > > Weinberg has the Eq.(6.10.1) to describe that effect.
> > > > The change in the distance betweens the balls is a
> > > > measurement of Curvature.
> > > > Regards
> > > > Ken S. Tucker
> > >
> > >
> > > This is one reason that I wanted to change the geometry...
> > > If you have a constant gravitational field, and you drop one ball
> and
> > > then the other, the first ball will be going faster than the
second
> > > one, say 1m/s faster, and although they are both accelerating,
the
> > > second one will always be going 1 m/s slower than the first one,
so
> > > they will be separating at a constant rate.
> >
> > Yes, but I intended to discuss differentials of
> > accelerations. The "speed" difference it trivial,
> > only caused by separate release times of the balls.
> >
> > > If you have a gravitational field, the lower ball will always
> > > experience a greater acceleration than the upper ball, so they
> would
> > be
> > > separating at an increasing rate.
> >
> > Yup.
> >
>
> I said something other than I meant here. The above should read "If
> you have a *radial or cylindrical gravitational field*, the lower
ball
> will always experience a greater acceleration than the upper ball, so
> they would be separating at an increasing rate." i.e. from a string
> mass, where the gravitational force is proportional to 1/r^2 or a
point
> mass, where the force is proportional to 1/r.

Those two proportions might be reversed, but anyway
point taken.

> With an infinite plane, there is no difference in force, no matter
how
> far you get away from the plane.

Agreed.

> > > However, if the upper ball is actually experiencing more time
than
> > the
> > > lower ball, it should in some way actually be catching up to the
> > lower
> > > ball as it falls, since it experiences the force of gravity for a
> > > greater amount of time.
> >
> > Don't know what you mean there, Baez has a FAQ on GR
> > using falling coffee grains that I think is really
> > good.
> >
>
> The clock speed difference between GPS satellite clocks and
earthbound
> clocks is due partially to acceleration differenc and partially due
to
> gravitational potential difference. If there is no difference in the
> force (because of the infinite plane geometry) then there will not be
> any clock speed difference due to acceleration difference; there will
> only be the component due to gravitational potential difference. And
> it should be this gravitational potential difference that describes
> exactly the clock speed difference of the upper platform and the
> infinite plane.

There are too many arbituary components, I'm bailing.

> My hypothesis, probably already proven or disproven somewhere in the
> vast library of books I haven't read, is that the clock-speed
> difference between a clock on the platform and the clock on the
> infinite plane would be equal to the clock speed difference on a
> "rigid" accelerating body with exactly the same geometry (if it can
be
> rigorously established what "the same geometry" means in this
context),
> and it is in this way that gravity is equivalent to acceleration.

Who the *** cares, you've transformed to a
hypothetical situation, where are you going?

> > > Okay, I just ordered Weinburg (and Schutz) through interlibrary
> loan.
> >
> > Weinberg is very thorough, it's among the few
> > text books I've read where I haven't found an
> > error, or poor judgement.
> > It's a tough book because of that, no cowtoe.
> >
> > Regards
> > Ken S. Tucker
>
> Well, as long as he doesn't try to tell me that linearly independent
> polynomials describe an infinite dimensional space of perpendicular
> axes, I should be alright. Nah, I'm just kidding. That's a fine
myth
> if you like it.

Tell the guy who plots x,y,z,t numbers he should
switch to infinite dimensions, then see how much
the experimental physicists will embrace your theory.

> I used to believe that any book a teacher or professor used for a
class
> was authoritative and complete. I've come to realize that to learn
> something new, I have to read enough different stuff so that the
pieces
> of the puzzle are created, then read more stuff to jostle the pieces
> into place. For me, reading the easy book first works much better.

For sure, if you're a student max out on tensor
analysis.

> Jonathan Doolin
> www.spoonfedrelativity.com

.

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