For the second time in the past month, Minute Physics is making a statement about what gets taught in introductory physics. It is consistent, but I still disagree. I have had too many interactions with people who want to discuss relativity (or quantum mechanics) and are either very confused or think its wrong, and this is exacerbated because they have no familiarity with classical physics.
I have no problem with telling students that what they are going to learn in introductory physics is an approximation, but the claim that presenting Newton’s gravitation equation is akin to telling students that the earth is flat is an exaggeration. If you go down that path, then what of all the other approximations that we make in physics? Speaking of a flat vs curved earth, do you really want to force students to solve trajectory problems on a curved surface rather than flat one? Is a frictionless surface a lie, or is it a convenient approximation to simplify a problem? And, on the topic of friction, should we really delve into the morass that is friction, rather than just say that it’s proportional to the normal force and try and get the big picture across?
I think the objections are wrong in a few different ways — One of the principles you learn in solving problems is how to ignore complications that do not affect the answer to the question. Also, learning physics through to relativity and other advanced topics takes years of study. Introductory classes carry with them the need to prune the information to fit, and convey the material that is most important to the students’ needs. Most of them don’t need to learn about relativity, which is why it’s not part of the introductory classes.
I agree. Simplifications and approximations are important in order to be able to learn the stuff. They are also important in actual work, too. The video mentions that Newtonian gravity may be good enough for getting from planet to planet, but isn’t “correct”, but doesn’t mention that working scientists and engineers therefore use Newtonian gravity when going from planet to planet because it works, even if “wrong”, and is much easier than solving the problem in GR.
Amusingly for the “Newtonian Gravity is wrong; flat Earth is wrong” discussion, in my intro physics class we started out with gravity being F= mg (not F= -GmM/r^2), which is, in fact, the correct formula for a flat Earth.
Fermi problems highlight “good enough.” The shape of maximum surface gravitation for a homogeneous isotropic mass distribution (radius = R, spherical coordinates [R, theta, phi]) is not a filled sphere, r(theta) = 2Rcos(theta), and rotate phi for 3D. The winner is r(theta) = 5^(1/3)Rsqrt[cos(theta)], in a small neighborhood around one point at 1.026 spherical value.
Should it be taught? No. A teaching text appendix countering Official Truth helps separate those who can from those who should. Those who can’t are diverse.
http://ajp.dickinson.edu/Readers/backEnv.html
Because reality is really, really interesting.
I don’t like the equivocation between Newtonian mechanics and a flat earth. One is completely true within its domain of validity, it simply remains incomplete on different scales. The other is objectively false.
How you can relate this two, I’ll never know.
Scaling is the key, but scaling is not part of introductory physics. For a good and accessible discussion of scaling laws, see http://hep.ucsb.edu/courses/ph6b_99/0111299sci-scaling.html
Simplifying assumptions carry the risk that small scale effects can erupt disastrously in larger scales to invalidate confidently ignorant calculations. Nonlinear dynamics in 3D, for example, where energy storage in kinky vortices makes smoothness impossible. A convincing rationale needs to be provided for ignoring effects from larger or smaller scales.