24.111 HW4. Due in class, W 3/2. PLEASE TYPE YOUR ANSWERS.

1. Read this transcript of a brief interview with the (then) editor of Scientific American. Find two sentences in which he says false things about the Uncertainty Principle. Quote those sentences. After each sentence, explain why it is false.

2. When we first discussed the Stern-Gerlach experiment, I suggested a "less conservative hypothesis": When a spin 1/2 particle encounters a magnetic field, it almost instantly turns to align, or anti-align, itself with the field. Explain why the two-path experiment and the Stern-Gerlach experiment together show this hypothesis to be false. (Explain yourself fully. Your answer should be longer than a sentence, more on the order of a paragraph.)

3. When we first discussed the two-path experiment, I discussed four hypotheses about what is going on during the experiment. One of them was: the electron (somehow!) takes both paths simultaneously. (i) Write down the reason I gave for rejecting this hypothesis. (ii) Is that reason also a reason to reject what the orthodox interpretation says is going on, namely that the electron is definitely taking one or the other path, but not definitely taking the top path, and not definitely taking the bottom path? Why or why not? (Explain yourself fully. Your answer should be longer than a sentence, more on the order of a paragraph.)

4. Consider a pair of electrons in the "singlet" state

(1/sqrt(2))|0up>|0down> - (1/sqrt(2))|0down>|0up>.

Notice that the probability that the left electron will be deflected up through magnets oriented at angle X is the same for every X. What is this probability? Use this fact to prove that the singlet state is not a product vector. (Hint: what can you say, in general, about the probabilities product vector assign to spin measurements on the left electron?)