The conceptual contribution of the history in learning physics: the case of optical spectroscopy

Introducing Quantum and Statistical Physics in the Footsteps of Einstein: A Proposal

“…should be given. The factor Z(ν) = 8πν 2 c 3 dν can be intuitively introduced as the "number of electromagnetic waves" of frequency ν per unit volume, with ε = k B T being the average thermal energy associated with each of them, hence equipartition tells us that the average energy density per unit volume is given by (2). Intuitively, the "ultraviolet catastrophe" can be understood by observing that the numbers of higher and higher frequency waves grows unboundedly, so equipartition assigns them exceedingly large amounts of energy.…”

“…Energy quanta associated with frequency low enough to ensure that hν k B T 1 (the temperature, which sets the scale of what is meant by "low enough", is considered fixed), therefore, are much smaller than the average thermal energy, hence the effect of energy quantization should be negligible. Indeed, we can use the fact that 10 , for small x, e x ≈ 1 + x, to show the distribution (1) reduces to the Rayleigh-Jeans law (2), which was obtained by a reasoning which ignored energy quanta. Notably, Planck's constant h is erased in the process.…”

“…To quantify these fluctuations we could consider all the possible differences ∆ε = ε − ε and average them with the Boltzmann distribution. Actually, since by definition ∆ε = ε − ε = 0 (the contribution of molecules with lower than average energies compensates that of molecules with higher than average energy) this will work if we take the squares (∆ε) 2 = (ε − ε) 2 . The average of this quantity, (∆ε) 2 is the so-called quadratic fluctuation, or equivalently its square root (∆ε) 2 if we want to keep the same dimensions, measures how much the energies of the molecules tend to be different from the average, that is, it measures how wide the probability distribution is.…”

“…It is well established that the history of physics can be helpful to teaching in multiple ways (see e.g., [2]). A first advantage of using history surely consists in the possibility of putting physics topics in context, by embedding them in the time in which they were developed and linking them with other disciplines, especially in the humanities, whose teaching is intrinsically historical.…”

“…Students in this way may get the idea that light quanta were introduced by Planck, and Einstein's contribution was limited to an application of this idea, while actually the concept was born in Einstein's work. The explanation of the photoelectric effect is of course a revolutionary contribution 2 (after all, it earned Einstein a Nobel prize) but it is, more often than not, the only contribution of Einstein that is mentioned. The deep difference between Planck's hypothesis of energy quantization and Einstein's hypothesis of light quanta is not emphasized enough.…”