Very early on in the Quantum Mechanics course I audited last year (second lecture in fact), the prof talked about the ‘collapse of the wavefunction’ saying no one understands it, mentioning 3 approaches — Einstein (hidden variables), Bohr (nothing is there until you make a measurement) and DON’T ASK — IT WORKS. That was as close as we got to the philosophical conundrums of quantum mechanics. The course was at an elite woman’s college, and to thank them for putting up with me, I gave each member a copy of the excellent “Entanglement” by Louisa Gilder, both because it was extremely well done (see the NYT book review by Galison) and because from the jacket photo, Louisa could have been one of the students in the class (she was Dartmouth ’00). See http://luysii.wordpress.com/2009/12/07/the-end-of-quantum-mechanics-the-course-that-is/
Excellent though it was, this year I’d have chosen the book under review “Dance of the Photons” by Anton Zeilinger. The jacket photo shows him in typical mad scientist pose, complete with gleam in the eye and crazed smile, reminding me of nothing more than my freshman chemistry professor — Dr. Hubert N. Alyea, a small boy trapped in a professor suit, who almost always blew something up in each lecture.
If you’ve nibbled about the edges of quantum mechanics and wonder what’s really going on with such things as (1) superposition of quantum states (2) Bell’s theorem and inequalities (3) Einstein Podolsky Rosen etc. etc. this book will tell you.
You are clearly in the hands of a master teacher (as well as an experimental and theoretical physicist). You really don’t have to know anything about quantum mechanics to read it. He starts with two freshman physics students (Alice and Bob) and has them try to figure out what’s going on. Each gets a box with a red and a green light, a computer to record the flashes the boxes make and the time they occur. The boxes are on either side of the Danube (Zeilinger is from Vienna after all) and between them in a sewage treatment facility is a black box, hooked by separate fiberoptic cables to Alice’s and Bob’s box. That’s it. Then the data (red and green flashes) comes in and they try to figure what lies underneath.
This starts on p. 58 and goes on for 100 excellent pages, as they look at their initial data, come up with an explanation, find that it doesn’t work, look at their data harder find something else, find that it almost works, go back an look at their data another way, come up with more and more explanations. Along the way we meet the famous Einstein Podolsky Rosen paper (EPR) and its objections to the statistical nature of quantum mechanics. This goes on for 100 pages. No, it’s not that complicated and detailed, but it’s a way of introducing you to the experimental facts slowly so you have time to think about what it all means (as Alice and Bob do). Then you are referred to an appendix (p. 270) which gives a derivation of the Bell inequalities using identical twins.
Along the way you get an explanation of local reality (which is really two things — locality and realism). Realism as defined in the EPR paper is just this — if you can make a measurement which consistently produces the same result (within experimental error) you are measuring something real, which exists outside your measurement. It doesn’t have to be that complicated. If every time you look up in the sky and see the moon, the moon is there whether you are looking or not. Locality is just the idea that measuring something at point A has no effect on the measurement of something else at point B. Both assumptions are incredibly reasonable. Quantum mechanics makes predictions directly in conflict with local reality. Experiment after experiment (many of which are carried out by Alice and Bob) shows that the predictions of QM are born out and that local reality is not the way the world works (at least at the level of small objects such as photons).
What Bell did was to derive an inequality based on the assumptions of local reality, which could be tested. I’ll try to go over Zeilinger’s derivation of Bell’s inequality using twins (the best way to understand anything is to try to explain it to someone else). This is post is long enough, so I’ll save this for the next post.
You may have heard of Schrodinger’s cat. The poor thing is in a box with a cyanide pellet which can be activated by radioactive decay. We can’t look inside the box. Quantum mechanics says that prior to a measurement to determine whether it is alive or dead, the cat is in a ‘superposition of states’ — e.g. both alive and dead. Here’s where you might need a bit of physical imagination to follow Zeilinger, because he describes experiments with photons and two beam splitters (he explains what they are and how they work) which essentially proves that a photon exists in a superposition of states prior to measurement. It involves the photon essentially following two paths at once. The explanation is leisurely (as are all the explanations in the book) and clear, but will take some work on your part (it stretches from pp. 67 – 87).
There’s lots more in this book, particularly about quantum teleportation, but these were the parts of greatest interest to me, because they cover things I never quite understood. The QM course I audited was excellent, but it veered away from matters philosophic, preferring to use quantum mechanics to show how atoms work (this was a course in the chemistry department after all).