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Re: CAUSATION IN PHYSICS



I see I failed to mail this.

Regarding Ludwik's comments:
... . John is
referring to idealizations in which F acts on a particle, or on a rigid
body. Leigh, on the other hand, was bringing a very persuasive
argument for "F being a cause of a" in non-ideal situations. The
center of mass of a real body does not start accelerating at the
same moment at which the force is applied. What do you think
about this argument, John? In the last message Leigh wrote:

<SNIP Leigh's comments>

As much as I think Leigh's point was clear, I don't think he meant to
claim (if I'm incorrect here about Leigh's thinking, I hope he would
correct me) that "The center of mass of a real body does not start
accelerating at the same moment at which the force is applied."

Of course everything David says is, as usual, correct, but I did mean
that. I'm thinking of the temporal step function application of a
constant force F to a surface of a solid rectangular block, the
simplest sort of example one uses to introduce the topic, and the
extension of the discussion of discontinuous acceleration. I should
have clarified it by stating that I meant the concrete embodiment of
the center of mass of the block, the atom at that point given for the
undistorted block. The ideal center of mass does start to move
according to F = ma, but of course F does not instantly rise to its
constant value either. I believe that, in practice, it is as
impossible to apply the hypothetical step function force as it is to
produce discontinuous acceleration. I think that in such cases that
unphysical hypothetical phenomena are proposed as conditions, one
should expect that problems will arise.

This problem cries out for a an instantaneous definition of center of
mass which is consistent with special relativity. It would be a waste
of my time (even at minimum wage) to go through the exercise of
developing one. What I want to say is that there is far too much
weight being given to the overinterpretation of F = ma.

The central objective of science is to describe Nature. Much of that
description is best accomplished in mathematical terms. It is evident
to many of us that there is a causal relation between force and
acceleration. The fact that the relationship is not manifest in the
mathematical expression of Newton's second law merely indicates that
the description is incomplete. There is nothing deep to be inferred
from the incompleteness of that description. Of course a mathematical
expression subsuming causality could be invented and applied here, but
that is unnecessary for those among us who take the causal relation to
be self evident.

Leigh