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.
An answer:" It says that certain properties of things have a kind of reciprocal relationship, in such a way that the more precisely you know the value of one of these traits, the other trait becomes less precise." -- this is false. It's not that the more precisely you *know* the value of one trait (eg position), the less precise the other *becomes*; it's: the more precise one of the traits *is*, the less precise is the other. He gets farther from the truth in the next sentence: "So, for example, the more precisely you know the position of a bullet at any one moment, the less precisely you know what its velocity is." Now the claim is all about knowledge, and suggests that the Principle says there are limits to what we can know about the position and momentum of a particle. When in fact you can know *everything there is to know*, namely, exactly how precise its position and momentum are. (I accepted other answers if you made a convincing case.)
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.)
Answer: If this hypothesis is right, then repeated stern-gerlach experiments show that if an electron has previously passed through magnets oriented at 0 degrees passes through magnets oriented at 90 degrees, it has a 50-50 chance of orienting itself so that it's "north pole" points "up," and 50-50 for "down." But if that's what happens, then half the time the electrons going through the two-path experiment should be deflected down. That is not what happens.
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.)
Answer: (i) The reason I gave was: when you "look inside" the experiment while it was running, you never find the particle on both paths (or: if you install detectors on the bumpers, you never get both detectors going off). (ii) No, it's not. It's true that when you look inside, not only do you never find the particle on both paths, you also never find it "not definitely on either path." You always find it on one or the other. But according to the orthodox interpretation that's because "looking" at the particle changes its state, "forcing" it to acquire a definite position. It is part of the weirdness of the orthodox interpretation that things can have indefinite positions, but never when you are observing their positions.
4. Consider a pair of electrons in the "singlet" state
Answer:The probability is 1/2. A product vector has the feature that it assigns probability 1 to an up outcome to some angle. So a vector that never does this cannot be a product vector.