Gas station without pumps

2011 November 10

The beauty of physics

Filed under: home school — gasstationwithoutpumps @ 00:46
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We increased the physics class time to 3 hours starting this week: 2 hours on Friday (mainly for lab) as before, plus an extra hour on Thursdays for discussing the text.

On 2011 Nov 3, the first day of the extra discussion, one student came up with a fundamental question: “Where is the beauty in physics?” He saw it as potentially useful, but he did not know where to look for the intrinsic beauty, the way he did in subjects he is used to studying (history, languages, music, math).

I’m not sure I have a good answer for him—perhaps some real physics educators could help me out.

What I told him was that physics was about finding very simple ideas that explained a lot. Elegance in physics comes from using very few ideas or formulas as first principles and using them to explain many phenomena. It is similar to the mathematical elegance of having very few, very simple axioms which allow huge numbers of interesting theorems to be developed, but with the extra constraint that the derived results have to be good models of the real world. I pointed out that there were probably only a dozen fundamental ideas in the whole physics book, and much of the book was dedicated to helping students internalize those ideas and be able to derive consequences of them. In all of chapters 1–3, we have only a few ideas:

• Momentum is mass times velocity (with a relativistic correction): $\vec{p} = m \vec{v} \sqrt{\frac{1}{1-\frac{|v|^2}{c^2}}}$.
• Force is the derivative of momentum (actually, this is hidden until Chapter 4, probably to allow the book to be used by students learning calculus concurrently—but my students found it simpler to think of it as the derivative from the beginning).
• Springs can often be modeled as linear: $\vec{F} = -k \vec{x}$.
• Gravitational attraction is inverse square: $F = G\frac{m_1 m_2}{r^2}$

There is also some terminology:

• Velocity is the derivative of displacement.
• Acceleration is the derivative of velocity.
• Impulse is difference in momentum at different times. Incidentally, the word “impulse” seems to me to be totally needless vocabulary. It is much simpler to talk about change in momentum and use $\delta p$, without introducing a new word.

I went on to say that physics and physicists have trouble with very complex systems (like biology or history), because there aren’t any simple fundamental ideas with enormous predictive power. Beauty in physics comes from recognizing how to simplify complex things so that simple models can be effectively applied. The only example we’ve had so far is the point mass, which is a great model for a bouncing ping-pong ball, but which would not work well if we had a soft squishy ball with a sticky surface. Other, more complicated models might be made to work—a lot of the challenge in physics comes from finding the simplest model that is adequate for the phenomenon being modeled.

1. Also–the beauty in physics is that it’s defined every where we look in the world around us! Gravity, velocity, acceleration–we can give direct examples in probably 5 different things we’re doing right now that involve physics. It’s an everyday science which is immediately applicable.

Comment by Dr. Keith Verner — 2011 November 10 @ 06:24

• So you see the beauty of physics in its applicability. But that would argue for teaching engineering, not physics.

Also, the student in question was not an engineering student. He started from the applicability of physics and then asked where the beauty was. He knew what was beautiful (for him) in other subjects he studied (music, foreign languages, history, and math), and was wondering what the core beauty of physics was. Applicability was not an adequate answer for him.

I have both a pure math and an engineering background, so I can see the beauty in both viewpoints. For this student, I need a “pure math” answer, not an “engineering” answer.

What makes a physics solution beautiful? It is not enough that it “works”—one can come with dreadfully inelegant rules of thumb that work. What distinguishes beautiful physics from ugly physics? How do physicists decide between hypotheses that fit the data equally well? What makes the warm glow inside that tells someone that this is what they want to dedicate their lives to?

Comment by gasstationwithoutpumps — 2011 November 10 @ 09:16

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