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Re: [Phys-l] Equations

Here's a mouse, at least.....
The transfer of virtual or actual particles between entities where in a frame of
interest there is a temporal dispersion between the object classified as cause
and that classified as effect, whereby the cause precedes the effect by some
time delay, and which is a sine qua non of the relation.

Brian Whatcott

At 11:04 PM 4/27/2006, you wrote:
Hi all-
I think that the elephant in the room is a missing definition. I don't
want to sound like a former president, but: What is the definition of
"cause"?
Regards,
Jack


On Thu, 27 Apr 2006, Dan Crowe wrote:

> I am deliberately expanding the conversation beyond Newton's second law (N2). John correctly states that causation implies asymmetry. My argument is that there is an asymmetry between force and acceleration. This asymmetry is not evident in N2, but N2 does not express all that can be said about the relationship between forces and acceleration. Based on information that is not contained in N2 - specifically that forces can exist in the absence of acceleration but acceleration cannot exist in the absence of forces - I conclude that forces cause acceleration but that acceleration does not cause forces.
>
> I agree with everything that John says about algebraic properties. We just disagree about the definition of causation. Because I believe that forces cause acceleration, I introduce N2 as a = (F_net)/m.* Eventually, we migrate to F_net = ma, because the analysis of free-body diagrams yields F_net, which we then set equal to ma. An equation is a relationship between variables, and both a = (F_net)/m and F_net = ma express the same relationship between the variables. After we make that transition, I use the form a = (F_net)/m only if I need to emphasize the cause-effect relationship or if I need to emphasize that ma is not a force.
>
> *For other pedagogical reasons, I actually use summation notation instead of F_net, but the limited character set available makes F_net more convenient for this email.
>
> Daniel Crowe
> Oklahoma School of Science and Mathematics
> Ardmore Regional Center
> dcrowe@sotc.org
>
> ________________________________
>
> From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of John Denker
> Sent: Thu 4/27/2006 6:37 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] Equations
>
> Dan Crowe wrote:
>> John Denker wrote, in part:
>> "Saying
>> F causes ma (1)
>> is just as true (or just as false) as saying
>> ma causes F. (2)"
>>
>> I continue to disagree. Forces can exist in the absence of
>> acceleration, but acceleration cannot exist in the absence of forces.
>
> You continue to misstate or misintepret the laws of physics.
>
> The F that appears in equations (1) and (2) is the _net_ force.
> I agree that acceleration cannot exist in the absence of net force ...
> but in the same breath I point out that net force cannot exist in
> the absence of acceleration. The force law equation is symmetric.
> This symmetry is precisely what sets equation apart from causation.
> Equation is symmetric. Causation is not.
>
> Nitpickers note: We continue to stipulate that m is nonzero.
>
> Rick Tarara wrote:
>
>>> My approach is to deal with Newton's First Law as expressing the
>>> causation--accelerations are caused by forces. [Try to accelerate something
>>> without a force!]
>
> Again I agree that acceleration cannot exist in the absence of net
> force ... but in the same breath I point out that net force cannot
> exist in the absence of acceleration. The force law equation is
> symmetric. This symmetry is precisely what sets equation apart from
> causation. Equation is symmetric. Causation is not.
>
>
> Michael E. wrote:
>>>> It's not a matter of one permutation being more correct, which, of
>>>> course, is not true. It's a matter of asking if one of the permutations
>>>> will make more intuitive sense to the students, and therefore it might
>>>> be beneficial to start with that one. I may be fooling myself, but I
>>>> think I = V/R and a = F/m are the more intuitive permutations of these
>>>> equations.
>
> This brings to mind the proverb about giving them a fish versus teaching
> them to fish.
>
> I understand why you might tell some students "a = F/m" whereupon they
> happily accept the yummy fish. And if the student is acutely starving,
> that might be a necessary starting point. But we must not stop there,
> or even pause there.
>
> The "fishing tackle" in this case comprises the basic rules of algebra.
> I'm not talking about rocket surgery; I'm talking about ideas like:
> a) equality is reflexive, symmetric, and transitive, and
> b) you can divide both sides of any equation by m (for nonzero m).
>
> These are ideas that are "supposed" to be introduced in ~7th grade
> (sometimes earlier) and "should" be pretty well consolidated by
> the time kids get to HS physics.
>
> IMHO if physics students don't understand those ideas, it is a matter
> of some urgency for those ideas to be taught and learned. Those are
> truly fundamental ideas. Trying to bypass those ideas is building
> the proverbial house upon sand.
>
>

--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley



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Brian Whatcott Altus OK Eureka!