The F=ma equation is short for F(t)=ma(t), and means the
force at a given time is proportional to the acceleration
at the very same time.
With remarkably few exceptions, the laws of physics are invariant
under a reversal of the time variable. F(t)=ma(t) has the same
meaning as F(-t)=ma(-t).
Exception #1: Thermodynamics has an arrow of time. Some of the
laws of thermodynamics are inequalities, not equalities.
Exception #2: Kaon decay is not invariant under time-reversal.
Exception #3: The expansion of the universe means the future is
different from the past.
Non-Exception: The causality restrictions of special relativity
are invariant under time reversal. The future light cone has the
same physics as the past light cone.
Non-Exception: Basic black-hole dynamics is invariant under
time-reversal (although there is black-hole thermodynamics also).
Question: Can you think of any other exceptions?
Item #1 (the thermodynamics exception) is the only one I can think
of that is even remotely relevant to a first-year mechanics course.
Symmetry arguments contribute a lot to the power (and the elegance)
of physics. Lying to students about the time-reversal symmetry of
F=ma and the other laws of mechanics is unnecessary and unhelpful,
to say the least.
Now, regarding causation itself, various views have been expressed:
Part I -- plain version. This is the version I recommend:
There is a very simple syllogism:
Major premise: a cause-and-effect relationship is asymmetric.
Causes strictly precede effects, and not vice versa.
Minor premise: the F=ma equation is symmetric. It has the
same meaning as ma=F.
Conclusion: F=ma does not express a cause-and-effect relationship.
Stronger conclusion: There cannot be a cause-and-effect relationship
between F and ma.
These conclusions are inescapable, given the known laws of motion,
and the foregoing major premise.
If a student asks whether F causes ma or vice versa, the answer
should be: "You can't have F without ma, and you can't have ma
without F. The relationship between them is called 'equality'
and is not properly called 'causality'. Equality is symmetric;
causality is asymmetric."
Part II -- stretched version. Some people seem to favor this version.
I don't recommend it, but I can tolerate it:
In this version, causes can either precede effects,
or coincide with effects.
As always, the F=ma equation is symmetric. F(t)=ma(t).
In this version, we choose to say that F is "caused" by ma.
By the same token, we say that a is "caused" by F/m.
The relationship between F and ma remains symmetric.
Part III -- plain Big-Endian version
Causes strictly precede effects (same as part I).
Big-Endians adjoin to the laws of motion an arbitrary assertion
that accelerations are caused by forces.
This version is blatantly inconsistent with the known laws of
motion, starting with F(t)=ma(t).
Part IV -- stretched Big-Endian version
Causes precede effects, or coincide with effects (same as part II).
Again, Big-Endians adjoin to the laws of motion an arbitrary
assertion that accelerations are caused by forces and not vice versa.
Meanwhile, Little-Endians adjoin the opposite assertion, that
forces are caused by accelerations and not vice versa.
In this version, neither assertion is false; both are vacuous.
Both are distasteful, because they imply that the laws
of physics are less symmetric than they really are.
Neither can be deduced from any useful theoretical principle.
There is no experiment a Big-Endian can do to convince a
Little-Endian, or vice versa.
Any physically-relevant calculation you can do using such an
assertion can be done equally well without it.
Big-Endians can employ PbBA (Proof by Bold Assertion):
"it is manifestly obvious that accelerations are caused by forces"
but we reject this as totally unscientific.
Big-Endians can appeal to scripture:
"accelerations are caused by forces because So-And-So said so"
but we reject this as totally unscientific.
Part V -- fortran version
Whereas in previous versions the "=" sign signified a
mathematical equation, in this version we let it signify
an assignment operator. That is, it represents the relationship
"calculated from" rather than "equal to" or "caused by".
In this version, it is easy to come up with examples where
F should be calculated from ma, and it is also easy to come
up with examples where a should be calculated from F/m.
Students should realize that the order in which things are
calculated has essentially nothing to do with the order in
which things actually happen. It cannot shed any light on
causality relationships.