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Re: [Phys-l] Equations (causal relationship)



While possibly opening myself to disdain, I seem to keep agreeing more with JohnD than the others.

Consider our old friend the frictionless inclined plane (inclined so the sliding object goes down to the right). Two forces: gravity, and one of constraint. Are there 2 accelerations or not? It seems to me the answer depends on the basis you choose. Mathematically it is common to choose an x-y (left/right and up/down) basis and write {F_x = ma_x, F_y = ma_y} and solve. Is one then required to state, in order to finish the problem or for any other reason, that the only "real" acceleration is the vector addition of a_x and a_y?

Put this in the classroom setting and use a camera, in two different frames of reference (if you like, use a virtually transparent inclined plane, or digitally remove it from the movie frames). In one instance, accelerate the camera down with the sliding object - the movie will most definitely show the object accelerating to the right. Likewise accelerate the camera to the right with the object, and the movie will most definitely show the object accelerating down, but with a value less than g.

In the classroom setting, speaking of pedagogy, you will be hard pressed to deny to the students that the two independent accelerations (right,down) are not real. In fact, you will have just done more to convince them of that fact than otherwise. They will immediately understand that depending on the frame of reference, you can either view the acceleration as one "total" single vector quantity, or two that can be added as vectors. In deference to JohnD, I can't see how one must be preferred over the other.

In deference to Brian, frame of reference is crucial here, but I can't see that it decides this question about 1 or 2 accelerations (in my particular example). In fact, it demonstrates the distinction and prevents an "absolute answer" from being posited.

I am curious as to the flaws others see in my POV. BTW, nothing here has anything to do with causality IMO. I suggest that JohnD's earlier note that F(t) = ma(t) is all that is needed to see that N2 in all its algebraic forms says nothing about causal relationships. Having said that, a looser definition of "causality" is a very useful pedagogical tool, because the students demand to see things in those terms. I see no issue with using the language to get a point across. For the deeper students, a deeper discussion of causality and how it relates (or not) to equations is appropriate, and becomes mandatory for those who seek careers in physics.


Stefan Jeglinski