On a whim, I made an end-of-semester lecture for my general physics class, which I
think could be taken in number of interesting directions. Near the end of the
semester we cover the basics of quantum mechanics, and it is the first time where the
students are presented with the notion that the equations make predictions, and we
don't always ask questions about what is "real". I realized that the same thing
happens in classical mechanics, where you have several different descriptions of the
same thing, but using different (although often related) underlying concepts, such as
force and energy, and one may start to ask which concept is (concepts are?)
fundamental, real, etc.
So I decided to look at the problem of a baseball thrown upwards and coming back
down, but try to see how many different descriptions I could think of for this same
problem. I came up with 5:
1) force: the ball experiences a force at every instance, which determines how the
speed changes, and thus the trajectory (space and time) of the ball
2) energy: the ball chooses the trajectory which makes the total kinetic and
gravitational energy constant at each point
3) least action: the ball chooses the trajectory which minimizes the summed
difference of KE and GPE over the entire trajectory (as if the particle plans the
whole path at the beginning)
4) general relativity: the ball experiences a local distortion of the space-time, and
follows the geometry
5) quantum gravity: the ball exchanges gravitons with the Earth, which influences its
path
certainly some of these could be rephrased to be shown as equivalent, but it is
interesting to look at the simplest problem from the most diverse perspectives. I
only did the 1st three quantitatively (numerically, for 3, using Taylor's least
action applets) but it would be interesting to see if many of them could be done
somewhat quantitatively.
the point here is to reinforce the idea that physics is a description of reality, and
the even if the concept is intuitive, it need not be "real" in any sense other than
being useful. Force seems more intuitive to many people, but energy is used
exclusively in QM.