Assignment 14: Atoms and the Quantum

John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh

For submission: Tuesday April 17; Wednesday April 18

1. How could there be any doubt about the atomic theory of matter as recently as 1905?

2. How did Einstein's work on Brownian motion make the atomic hypothesis credible?

3. In 1905, Einstein proposed that light sometimes behaved as though it consisted of spatially localized quanta (i.e. lumps) of energy. This is his "light quantum hypothesis." Nowadays everyone knows Einstein was right and light consists of what we now call photons, the more modern term for Einstein's light quanta.

What was so shocking about Einstein's proposal when he made it in 1905?

4. Einstein's basic argument depended on an analogy with ideal gases that went as follows.

(a) If we have a single gas molecule bouncing about in a chamber, what is the probability that at any one moment it will be found in the left half of the chamber?

(b) If we have 100 gas molecules bouncing around in the chamber and if we assume that they don't interfere with each others' motions at all, what is the probability that they are all to be found at some moment in the left half of the chamber?

(c) Einstein investigated the thermodynamic properties of an amount of high frequency heat radiation of some definite Energy and frequency. From it, he was able to figure out that the probability that it would spontaneously compress to half its volume. That probability proved to be (1/2)^{Energy/(h x frequency)}, where h is a universal constant, now known as "Planck's constant."

How does comparison of this probability with the result of (b) enable Einstein to arrive at the light quantum hypothesis.

For discussion in the recitation

A. It is not so easy to prove that there are atoms. What experiment would you devise to prove the reality of atoms?

B. Imagine that you were transported back to antiquity and you confronted the mainstream of thinkers who doubted there were atoms. How could you convince them of the reality of atoms? No appeals to authority or what will happen in the future work. You have to use arguments they can follow of make demonstrations that they can see.

C. While the main argument Einstein gave for his light quanta is summarized above, the most famous argument of his 1905 paper on the light quantum dealt with the photoelectric effect. Indeed his explanation of the photoelectric effect was cited in the award for Einstein's Nobel prize. What was that argument?

(This is not covered in the lecture summary. See J. P. McEvoy and Oscar Zarate, Introducing Quantum Theory. Icon Books. p.44+ for an explanation that is a little convoluted. Try also the internet, which has many sites explaining it.)