This World Wide Web page written by
Oberlin College Physics Department;
last updated 7 December 2006.
I also received helpful direct comments from Joe Palmieri and Robert Romer.
Insert the following paragraph before the paragraph that begins with "Imagine, for example . . .":
Here is a straightforward proposal that explains most of these observations: Simply suppose that when the pairs of atoms are produced, one atom has mz = +mB and the other has mz = -mB. This proposal explains the first four observations, but it is inconsistent with the last one. If the two analyzers are, say, horizontal instead of vertical, then under this proposal it would be possible (see problem 6.2) for both atoms to leave through their + exits, or for both to leave through their - exits. But in fact the two atoms always leave through opposite exits. The straightforward proposal is appealing, but it must be wrong. Eventually we will replace this straightforward yet incorrect proposal with a much more elaborate one, a proposal called "quantum mechanics". For the time being, however, it is important to get a clear idea of how atoms actually do behave before rushing into new proposals. So how do the atoms behave?
The article mentioned on this page has been published as
The Hardy experiment has been performed! This exciting development is described in my essay Hardy's test of quantum mechanics. (Reading this essay requires the free Adobe Acrobat Reader software.)
The pressure of sunlight is responsible for the tails of comets: these tails always point away from the sun.
Quantal interference has now been observed experimentally in molecules as large as C60, the "buckyball"! See
A new and well-received popular account of superstring theory is
An additional problem for chapter 10:
If the standard interference experiments 9.1, 9.2, and 9.3 are repeated with the interferometer tilted by an angle q instead of by 90 degrees, then the probability for passage from input to output is 0 if both branches are unblocked and is sin2(q/4) if either branch a or branch b is blocked. If an atom with mz = + mB enters such an interferometer, what is the amplitude for taking the top branch? The bottom branch?
[This question was inspired by Kyla Pasha, a very thoughtful student who took my course in the fall of 1998. She found the interference results disturbing because, in the situations mentioned in the book, there was either (1) all amplitude to go through one branch and no amplitude to go through the other or else (2) equal amplitude to go through either branch ("the atom goes through both branches"). She was relieved to find out that there were situations with more amplitude to go through one branch than the other, and hence a gradual transition from situation (1) to situation (2).]
I state that blackbody radiation explains "why a gas stove should be adjusted to make a blue flame". This is wrong. The blue flame comes from 431.5 nanometer chemiluminescence radiation from carbon-hydrogen bonds, not from blackbody radiation. [See A.G. Gaydon and H.G. Wolfhard, "Flames: Their Structure, Radiation, and Temperature" fourth edition (Chapman and Hall, London, 1979) pages 252-256.] I thank Professor Douglas Marcum of Miami University for correcting me on this point.
Those interested in quantum computers and quantum information processing will also enjoy the articles
Quantal entanglement plays a central role in the popular thriller
The 1998 Tony-award-winning drama "Copenhagen", by Michael Frayn, involves "a wide-ranging, intensely emotional consideration of everything from quantum mechanics to the loss of a child" (Ben Brantley, New York Times, 12 April 2000).
Also of interest is the play "Now Then Again: A New Comedy About Love, Coffee and Quantum Physics", by Penny Penniston.
The trilogy "His Dark Materials" by Philip Pullman is rich in quantum mechanical themes. Book two, The Subtle Knife, mentions Everett's 1957 "many-worlds formulation" of quantum mechanics on page 242. Book three, The Amber Spyglass, mentions quantum entanglement on page 175. (The book incorrectly suggests that entanglement could be used to send messages instantaneously -- this is good fiction but in fact wouldn't happen.) The third book is in fact named for an instrument (an amber spyglass) that is one version of an interferometer (pages 225-231).
The Center of Things by Jenny McPhee is a "novel about true love and modern physics" featuring "a freelance intellectual in blue pajamas who is happy to chat about quantum mechanics in the library stacks" (Scott Veale, New York Times, 3 November 2002).