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Re: [Phys-l] The nature of force fields.

I have no quarrel with John's reply, I would have stated it more succincly.
A force field is a vector field (a mathematical concept). A vector field assigns a vector to each point of space (at a particular time). The vector is the force, associated with the point.
I have high school students illustrate this concept in class by rising, on commant, with each student holding out his/her arm, pointing in some individually chosen direction. The students are illustrating a vector field, each arm denoting a vector associated with the point where the student is located.




On Thu, 10 May 2007, John Denker wrote:

On 05/10/2007 03:13 AM, Tibor G Molnar wrote:

It occurs to me that the definition of 'force fields', such as
gravitational fields, is circular.

I prefer to think of it as incomplete rather than circular.
See below for details.

When we ask "what is a force field?",
we are told that it is a region of spacetime where some or other material
object experiences a force. And when we ask "how/why does an object
experience a force in some region of spacetime?", we are told that it is
due to the presence of a force field.

But what is a force field "really"? In order to exert a force (whether
pushing or pulling) on material objects, a force field needs logically to
be the effect of some or other real, physical "goings on". But what? Do
we have a mechanical, causal explanatory account of what a force field
"actually" is?

More particularly, how can I understand (without ultimately appealing to
some or other Einsteinian "spooky action at a distance") how, in the case
of gravity for example, one physical object can remotely 'pull' another?
To pull something, don't we need a line with a hook on the end?

I am familiar with Einstein's explanation in terms of warped spacetime; but
as far as I can tell, that is just an instrumentalist account, with little
causal explanatory power. Is there a better explanation?

In a small way yes, there are more-detailed explanations
for each of the known forces. But if I gave you the
more-detailed explanation, you would just re-ask the same
sort of questions at a more-detailed level.

So the big answer is that such questions are by-and-large
unscientific. This is one of the big breakthroughs that
Galileo made: He realized that it sufficed to say what
would happen under such-and-such conditions; he did not
need to say /why/ it happened.

Specifically:
The present does not seem to me to be an opportune time to enter
into the investigation of the cause of the acceleration of
natural motion, concerning which various philosophers have
produced various opinions ....
Such fantasies, and others like them, would have to be
examined and resolved, with little gain. For the present, it
suffices .... to say that in equal times, equal
additions of speed are made.

Galileo, _Two New Sciences_ (1638).

This was a major departure from how things had been done previously.

Newton echoed this point more concisely in his famous pronouncement
"hypotheses non fingo".

The question of "what happens" is physics.
The question of "why" is (usually) metaphysics.
If people want to discuss metaphysics, that's OK; I just ask that
they not get in my way when I'm trying to do physics.


It is important to distinguish between nature and models. First,
last, and foremost, nature is what it is, and does what it does.
Meanwhile, models are made by people for people, to help us predict
what nature is going to do. All the models are imperfect.
-- You are free to ask for a more-detailed or less-detailed model.
Electrostatics? Classical electrodynamics? Quantum electrodynamics?
Take your pick.
-- You are free to ask whether a counterintuitive model could be
made more intuitive ... but this is a moving target, because as
the proverb says, education is the process of cultivating your
intuition.
-- You are free to ask whether this-or-that model is consistent
with some other model, and/or consistent with observations.
-- All models are imperfect. It's not helpful to complain about
this-or-that model unless you've got something better to offer.

Asking for a "mechanical" model of what's going on is almost certainly
a step in the wrong direction. Lots of people have tried over the
years, and the uniform experience is that the mechanical models work
less well than the more abstract field models.

Mostly we write field equations because we can. They are mathematically
tractable and do an excellent job of predicting what will happen under
a large (albeit not infinite) set of conditions.

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General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley