Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

[Phys-l] Student axes problems (Was: heads up: Conformal Geometric Algebra)




In particular, CGA provides the answers to some questions
that have been bugging me for decades. For starters,
consider the fundamental principle that physics is
independent of absolute location. We are free to choose
an origin of coordinates, but somebody else might choose
differently, and all the fundamental equations of physics
really ought to come out the same. This is an example of
gauge freedom. This independence has been known for a
long time; it predates Galileo's principle of relativity.


This particular concept is very problematic with students. In particular
they have difficulty when you cross over the origin. I have firm evidence
that when you go from the positive to the negative side of the axis that
many students then switch the signs of some other kinematic quantities.
They have no problem as long as you stick to the positive side of the axis.

This seems to correlate with similar sign misconceptions so that when
velocity switches sign they will often want acceleration to switch also. It
is clear that the way math treats the origin as a "special" place is in some
ways the problem. Also students are not asked from the beginning to pick
their own axis and then state where it is located.

The idea that the physics is independent of both the position axis and the
velocity is very difficult for students. Just telling them about Galilean
relativity does not fix the problem.

I realize this is not CGA, but the post sparked this observation.

John M. Clement
Houston, TX