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Re: centrifugal force



Well, I'll try just a bit more, but we are talking past each other.

Leigh Palmer wrote:

It is generally acknowledged that the "source" of the gravitational
force is the gravitational field at the point in question.

That begs the question. What is the source of the gravitational field?
It is clearly another body.

It may be clear to you, but the guy in the laboratory can't tell
without recourse to outside observation. That is the whole point.

The centrifugal "force" does not have
another body as its source!

So what? The guy in the lab doesn't have access to that
information either.

It is caused by rotation against absolute
space, unless you want to adopt the radical view of Mach that it is
completely equivalent whether the observer's frame rotates relative to
the fixed stars or the stars rotate around the observer. In order to say
that centrifugal force has an agent (i.e. another body as its source),
trhe only bodies available to cause that "force" are the "rotating"
stars -- talk about action at a distance!

(I'm afraid I don't understand this part.)

If you
believe otherwise then you adopt an action at a distance model.
Such models are cognitively troubling, and there is evidence that
they are unphysical. I have previously cited the ptroblem that
arises if one considers the source of the gravitational force which
acts on the Earth to be the Sun, without the intermediary agency of
the gravitational field.

This has nothing to do with the subject under discussion. No one --
least of all me -- suggests action at a distance without a field. That
is irrelevant to the question of the reality of inertial forces.

Oh? Someone was talking about a criterion for reality based upon
Newton's third law. I thought it was you.

If there is nothing in contact with the body then you are in an
inertial frame; you've got it! Why do you consider that to be
circular?

What? If you are rotating with respect to the fixed stars and there is
nothing in contact with you, you consider that to be an inertial frame?

No. That can only occur if the axis of rotation passed through my
center of mass. I will be in lots of different non-inertial frames,
won't I? I suppose there will be a set of volume zero of places
where the frame is inertial (on the instantaneous axis of rotation)
and I'd think some more about it, but you've placed me in a frame
that makes my head hurt. What's your point?

I'll try once again. In order to decide whether you are in an inertial
frame -- by an experiment -- you must look at a body which is force free
and see whether it continues in uniform rectilinear motion. If it does,
you say the frame is inertial. If not then it is not inertial. The
problem is: how do you decide that the body you are watching is force
free? The fact that nothing is in contact with it does NOT prove it is
force free.

You have completely missed the point. I'll know there is no *net*
force acting on the particle if it does not accelerate. (I prefer
to consider a particle at rest because it stays in my frame. If
I must contemplate a moving particle I shall do so from a comoving
frame. Frames in uniform motion with respect to an inertial frame
are also inertial. Think only about resting particles by
transforming away uniform motion.) If the particle does accelerate
I will know I'm not in an inertial frame. If I gave the idea that
a particle under consideration was "force free" I apologize. I can
only say something about the net force acting on the particle.

Suppose a) you find that the body you observe is
unaccelerated and you see no obvious force on it. There are two choices:
1. Your frame is inertial and the body is indeed force free. 2. Your
frame is in free fall in a gravitational field. Those two
interpretations are indistinguishable experimentally; one leads you to
conclude that your frame is inertial and the other that it is not
inertial.

No, no, no! Indistinguishability is the operative criterion here.
If the particle doesn't accelerate with respect to a frame then
that frame is inertial. You have no choice (or the trivial "one
choice").

Centrifugal force is a little different only in that it requires a
peculiar gravitational field to explain it away. So again let's say we
see an apparently force free mass undergoing acceleration -- this time
radially outward.

"radially outward" from what?????

As always there are two possible interpretations:

As always? Why must there always be two interpretations? Where
is it written that there is a canonical duality? How about a
trinity. eh?

This is indeed frustrating; we are talking past one another.

I give up!

Leigh

1.
Your frame is rotating (non-inertial). 2. Your frame is inertial but
there is a radial (outward) gravitational field. The second requires a
postualte of a strange distribution of matter in the neighborhood but
violates no law. I repeat: there is no absolute way to decide whether
your frame is inertial by local experiments -- though in the centrifugal
(and Coriolis) cases it is obviously more convenient to assume absolute
rotation of the frame rather than some diverging gravitational field.
(This may in the future have to be modified actually because of the
microwave background radiation -- see below.) Because of the property of
gravitation that it produces the same acceleration independent of the
mass, one can always explain away an apparent effect of a non-inertial
frame (locally) by postulating the appropriate gravitational field,
though it requires some mighty peculiar fields to do so in some cases.

It was clear many decades ago that there is no absolute way to decide
whether you are in an inertial frame.

To whom was this clear? Please cite the enlightened source.
I have just explained exactly how to decide whether or not you
are in an inertial frame.

There is a good discussion of the foundations of mechanics, and
especially the concept of inertial frames in Phillip Frank's "Philosophy
of Science" dating from about 1950. I believe it is also discussed in
Sir Arthur Eddington's "Space, Time, and Gravitation" (not later than
the 1950's possibly earlier). Einstein discusses the issue, though not
exactly along these lines, while discussing the reasoning that led him
to General Relativity. See the autobiography in the Schilp volume
"Albert Einstein -- Philosopher Scientist" (P.A. Schilp ed., 1949). ANd
of course there is the work of Mach himself (100 years ago!) that was
quite influential on Einstein.

Are these "enlightened" enough for you?

The only thing that is clear is that there is no *unique*
inertial frame without external reference. Of course the
comoving frame of the Hubble flow is a unique frame, but one
cannot detect the Hubble flow locally, within a closed
laboratory.

Well maybe you can. The microwave background does seem to provide a
preferred frame, and one can measure one's velocity relative to that
frame by looking at the Doppler shift of the microwave background in
various directions.

Don't know if this has helped us get on the same wavelength, but that's
enough on this one.