## Thursday, March 12, 2015

### Teaching students to be more critical

One on the many disturbing things I find about science today is people claiming that because a particular theory agrees with a particular experiment that the theory must be valid.
Little consideration is given to the possibility that the agreement may just be an accident. The "correct" theory may actually be quite different. They may be getting the "right" answer for the "wrong" reasons.
I am never sure if the people who make these kind claims are sincere, naive, and/or just engaging in marketing.
Students need to be taught to be more critical.

I am currently teaching an advanced undergraduate course on solid state physics, PHYS4030. It follows Ashcroft and Mermin closely.

I have just taught the Drude and Sommerfeld model. Drude provides a nice example of getting the "right" answer for the "wrong" reasons. In both models the thermal conductivity is given by the following expression from kinetic theory
where c_p is the specific heat capacity and u_f^2 denotes the average kinetic energy of the heat carriers.

In Drude, the first factor is independent of temperature and "large", being of order k_B.
The second factor is proportional to temperature, and "small".

However, in the Sommerfeld model, which gets the physics correct, the specific heat is proportional to temperature, "small", and of order k_B T/T_F, where T_F is the Fermi temperature.
The average kinetic energy is independent of temperature and "large", being proportional to the Fermi energy.

The different terms in the Drude model are off by a factor of order one thousand, but these errors cancel beautifully so it gives an answer that agrees with Sommerfeld and with experiment to within a factor of two!

I stressed to the students that this is a good example how sometimes you get the right answer for the wrong reason. The fact your theoretical model agrees with a particular experiment does not prove it is correct.

This underscores the need for the method of multiple working hypotheses.

#### 1 comment:

1. Very nice point ... although now I'm going to take a cheap shot: imagine the day when a string theorist comes to this stage of saying that their theory only accidentally agrees with experiment!