Re: CAUSATION IN PHYSICS

[John Denker <jsd@MONMOUTH.COM>]

At 09:45 PM 10/9/00 -0400, Ludwik Kowalski wrote:

> In my presentations F is a CAUSE of acceleration. Mass is the
> same no matter how large the force (classically). A given force
> acting on a different m produces a different a. Simultaneity and
> rigidity are implied. Is this wrong in the first physics course? If
> so then why? Likewise a dop, for example from a battery, is a
> CAUSE  of current. That is a common approach, I suppose.

I suppose it is common, but it is not right.

The expression F = ma uses the "=" sign which represents the "equality"
operator.  Formally, equality is member of the class of _equivalence
relations_, because equality is reflexive, symmetric, and
transitive.  Reference:
  http://www.ms.uky.edu/~carl/ma502/html/green1.html

In contrast, the usual notion of "causation" is not symmetric or even
reflexive.  The notion of causation implies a partial order which is
incompatible with being a symmetric relation.

        (BTW note I said "causation" which is what people are talking
        about here, and is not quite synonymous with "causality".)

As second example of something that is not an equivalence relation, when A
is "equal by definition" to B I like to write that as
        A := B
using the ":=" symbol which has a non-symmetric appearance to make it plain
that "equal by definition" is not symmetric.

=========================
Now, applying these ideas to the current topic:

The physics expressed by "F = ma" is in fact symmetric;
        F implies ma
no more and no less than
        ma implies F.
You can't have one without the other.

In some circumstances we may _choose_ to calculate ma from F.  The ordering
of the chain of calculation bears some semblance to the ordering we would
expect from a chain of causation.  But it is merely a superficial
semblance.  In mechanics, the order of calculation is merely a choice for
the convenience of the person doing the calculation, and proves nothing
about whether the physics in question has a corresponding ordering.

Feynman wrote about this in _The Character of Physical Law_, starting at
the top of page 46.

If you work at it, you can find physics formulas that are not equivalence
relations (hint: thermodynamics).  But the "=" in "F = ma" remains an
equivalence relation:  symmetric, reflexive, and transitive.