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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.