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Re: Causation in Physics: F=ma



On 11/14/2003 05:17 PM, Folkerts, Timothy wrote:
>> I have a particle of mass (m) in a centrifuge.
>
> I have a satellite of mass (m) in an orbit.

OK.

>> Everything in the centrifuge is subject to an acceleration (a),
>> perhaps 10,000 Gees.
>
> Everything in that orbit is subject to perhaps 0.5 Gees

OK.

>> I can calculate the force on the particle according to the formula
>> F=ma.
>
> Ditto.

Yes.

>> Do you really expect anybody to believe that the force causes the
>> acceleration?
>
> Do you really expect anyone to believe that the gravitational force
> causes the acceleration?

No, or so I hoped.

> Well, yes, I do expect that (at least in a Newtonian point of view).

Sorry to hear that ... but based on what follows, I
suspect that belief is well on its way to changing.

> Are you saying that there is something special about the centrifuge?

Absolutely not. There is a profound analogy between
centrifugity and gravity which has been skillfully
and correctly exploited above.

> Or that all circular motion problems could better be thought of in
> terms of "accleration fields" instead of forces?

The key idea is that the gravitational field is not
a "force" field. It is a force per unit mass, so it
is properly called an acceleration field. The same
is true of the centrifugal field: it is an acceleration
field.

>> The acceleration is the same even if there is no particle at all!
>
> This is an interesting concept. Can "nothing" have a position or a
> speed or an acceleration?

An empty point in space can certainly have a gravitational
field.

> Don't you need "something" as a reference point?

-- You do need to specify a reference frame.
-- You don't need a test particle at the given point.
(Details below.)

> How do you measure the acceleration of "nothing"? On the
> other hand, I have no trouble talking about E fields without needing
> a particle to interact with it. This bears a little more thought.

I think TF has essentially answered his own question.
The status of the E field is the same as the status of
the g field and the centrifugal field. There are at
least three good ways to think of defining the field:

1) You can imagine measuring it with a test particle,
then abstracting away the test particle.

2) If you know the sources, you can calculate the
field _ab initio_, using the famous formula.

3) If you don't know the sources, but you know that the
region of interest is source-free, you can measure the
field on the boundary of the RoI and interpolate. It's
a simple differential equation with Dirichlet boundary
conditions.

Note that in all cases (E, g, centrifugal) the value
of the field depends on the choice of reference frame.