Re: CAUSATION IN PHYSICS

["John M. Clement" <clement@HAL-PC.ORG>]

While the math is undoubtedly correct, one must remember that the math is merely one description of the relevant physical situation.  Causation is a judgement, and not necessarily a mathematical fact.  From this point of view it makes sense to say the following.  Bob pushed on the car, as a result it accelerated.  However, "The car accelerated, as a result Bob pushed on it" does not make sense.  Yes, the math does not recognize the illogicality of the second statement.  And yes the push and the acceleration are simultaneous and the equation does not recognize causation.  However to push Bob had to first move his hand prior to the acceleration, thus establishing causality.

The real reason for establishing the causation link between forces and acceleration is ultimately pedagogical.  Students who do not establish this link usually exhibit very fuzzy thinking.  Unfortunately they do not think in terms of math relationships.  They must first make a link that acceleration is caused by force, then they must make the reverse link that when you observe acceleration, you know there must have been a force.  Making one link does not automatically establish the other.  Later on in a very advanced course they might understand that the mathematical description does not need causation.  Part of this problem is caused by the fact that most HS physics students and many college physics students are not formal thinkers.  As a result they do not really understand equations with 3 variables.

Do I have any proof that this type of reasoning actually helps students?  No.  As far as I know nobody has tried to teach this both ways and done the appropriate pre and posttesting to establish a link between using a causal or non causal explanation and a desirable outcome.  My intuition, and interviews with students lead me to believe that using causation helps students make the desired connections.  Perhaps some of the other readers of this list have some relevant research that they can cite to establish the best method.  In either case my good posttest scores validate my approaches, so I will stick with them, until I learn better methods.  I would also like to submit that criticism of a pedagogical approach is only truly valid when tests can substantiate which approach works better.

Now when it comes to Newton's third law (NTN3), the symmetry of the relationship negates any attempt at establishing causation.  As a result the traditional questions that are often asked by teachers about which is the action and which the reaction should be burned, and those teachers should be flogged.

John M. Clement
St. Pius X HS, Houston, TX


> > 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.