The "Live Cat Dead Cat" superposition equation that appears in A Serious Man (see my Back to the Cat and Back of the Cat blog entry from last year) also shows up in the November 1975 issue of the American Journal of Physics--the only other place I've seen it--in a short paper by a fellow named Asher Peres. I don't know if he was (he died in 2005) related to the current president of Israel, Shimon Peres, but that is not our concern of the moment. (However: he wasn't. See Wikipedia article about him.)
Our concern is partly that I just stumbled upon this article and equation while looking over some old discarded issues of the AJP that I picked up when I worked as a lab assistant at Austin Community College in the 1990s. Our other concern is for the physics involved, and whether these old 1975 statements would be legitimate today. What statements? Oh, just that dead cats might be made alive again (the question of whether this could happen exactly nine eight times is not addressed).
So, first we have Asher
publishing his 1974 AJP paper (which I don't have a copy of, yet) called “Quantum Measurements are Reversible,” then we
have P. J. van Heerden of Polaroid Research Laboratories, Cambridge MA,
in the November 1975 AJP, on pages 1014 and 1015, complaining about this particular statement in Peres’ 1974 paper: “An ensemble of identical systems is in some
state, but a single system has no state.” P. J. v H. retorts “I believe that this statement
is incorrect,” and he goes on to give an example he claims shows that “single
systems do have eigenstates,” which is the title of his paper.
So then in response Asher pipes up in the following paper, “A single system has no state,” on pages
1015 and 1016, with, among
other responses to P. J. v H.'s paper, this paragraph: “Most
puzzling is van Heerden’s statement, ‘one can even think of an experiment
exhibiting the interference pattern between the cat alive and the cat
dead.’ If such an experiment could
indeed be performed, then the phase θ
in the state
ψ = 2-1/2[
|live> + exp(iθ)|dead>]
would be meaningful. One could then resuscitate dead cats in the
following way: Take an ensemble of dead
cats and measure on each one of them the projection operator on state ψ.
In 50% of the cases, the state of the cat will become ψ.
Now measure whether the resulting cat in state ψ is alive or dead. In 50% of the cases, it will turn out
alive. I did not say this is impossible,
but only that I don’t know how to construct the ψ-measuring machine.”
Were the Coen Bros friends with Asher Peres? Asher's homebase was Technion-Israel Institute of Technology, in Haifa, so it's unlikely that the C brothers and A. Perez crossed paths. Ethan and-or Joel may have heard second hand through the Jewish physicists' grapevine about the outrageous idea of reviving dead cats using the superposition equation for the live and dead states with the extra ingredient of a phase factor multiplying the dead "ket."
Sorry, that's a stupid pun, but an accurate one, because our old untalkative pal, PAM Dirac, invented a terminology that is now universally used in quantum mechanics where |a> is called a ket and <a| is called a bra. Bras and kets, which are vectors, often get multiplied together, most often with the bra vector first. Whadda ya got then? Bra-ket, or bracket! And also, you have "bras" appearing in a pointedly bra-like way in the equations of physics.
Asher Peres spent some time, on sabbatical, at the University of Texas at Austin, in 1979 or 1980. His Physical Review paper from 1980, called "Can We Undo Quantum Measurements?" appears in a book I have (Quantum Theory and Measurement, published in 1983 and edited by J. A. Wheeler and W. H. Zurek). I haven't made much sense of this paper yet, due partly to my ignorance of the subject and partly to the fact that it isn't very well written. The latter happens a lot in physics papers, and books. Or does it just happen a lot in general? Yeh, it may not just be your stupidity that keeps you from understanding something! Maybe the article or book is just poorly written, or written in such a pedestrian manner as to be sleep inducing. Stephen Hawking has confessed to not doing a very good job with the writing in A Brief History of Time, probably the most purchased yet unread physics book of all time. Most others who don't write well don't bother with the confessions.
(My profile lists science and math books that I think are good.)
(My profile lists science and math books that I think are good.)
Anyway, at the end of that 1980 paper Peres says: "I am very grateful to J. A. Wheeler for the warm hospitality of the University of Texas and to E.C.G. Sudarshan for many stimulating discussions. The final version of this paper has benefitted from comments by J. S. Bell (CERN) and A. Ron (Technion)."
I'll be discussing John S. Bell and his famous theorem later. A well-written article by a fellow named Travis Norsen concerning Bell's theorem just recently appeared in the American Journal of Physics. The AJP is not for publication of professional original results, which appear in other journals--you know, those "professional" journals such as Physical Review Letters or Nature or countless others (and also of course online at open access sites)--but is instead at the level of "pedagogy." But Norsen's article does break new ground nevertheless, I think.
