Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part One Reference Frame Columns, Physics Today 1988–2009
- 1 What's wrong with this Lagrangean, April 1988
- 2 What's wrong with this library, August 1988
- 3 What's wrong with these prizes, January 1989
- 4 What's wrong with this pillow, April 1989
- 5 What's wrong with this prose, May 1989
- 6 What's wrong with these equations, October 1989
- 7 What's wrong with these elements of reality, June 1990
- 8 What's wrong with these reviews, August 1990
- 9 What's wrong with those epochs, November 1990
- 10 Publishing in Computopia, May 1991
- 11 What's wrong with those grants, June 1991
- 12 What's wrong in Computopia, April 1992
- 13 What's wrong with those talks, November 1992
- 14 Two lectures on the wave–particle duality, January 1993
- 15 A quarrel we can settle, December 1993
- 16 What's wrong with this temptation, June 1994
- 17 What's wrong with this sustaining myth, March 1996
- 18 The golemization of relativity, April 1996
- 19 Diary of a Nobel guest, March 1997
- 20 What's wrong with this reading, October 1997
- 21 How not to create tigers, August 1999
- 22 What's wrong with this elegance, March 2000
- 23 The contemplation of quantum computation, July 2000
- 24 What's wrong with these questions, February 2001
- 25 What's wrong with this quantum world, February 2004
- 26 Could Feynman have said this? May 2004
- 27 My life with Einstein, December 2005
- 28 What has quantum mechanics to do with factoring? April 2007
- 29 Some curious facts about quantum factoring, October 2007
- 30 What's bad about this habit, May 2009
- Part Two Shedding Bad Habits
- Part Three More from Professor Mozart
- Part Four More to be Said
- Part Five Some People I've Known
- Part Six Summing it Up
- Index
7 - What's wrong with these elements of reality, June 1990
from Part One - Reference Frame Columns, Physics Today 1988–2009
Published online by Cambridge University Press: 05 January 2016
- Frontmatter
- Dedication
- Contents
- Preface
- Part One Reference Frame Columns, Physics Today 1988–2009
- 1 What's wrong with this Lagrangean, April 1988
- 2 What's wrong with this library, August 1988
- 3 What's wrong with these prizes, January 1989
- 4 What's wrong with this pillow, April 1989
- 5 What's wrong with this prose, May 1989
- 6 What's wrong with these equations, October 1989
- 7 What's wrong with these elements of reality, June 1990
- 8 What's wrong with these reviews, August 1990
- 9 What's wrong with those epochs, November 1990
- 10 Publishing in Computopia, May 1991
- 11 What's wrong with those grants, June 1991
- 12 What's wrong in Computopia, April 1992
- 13 What's wrong with those talks, November 1992
- 14 Two lectures on the wave–particle duality, January 1993
- 15 A quarrel we can settle, December 1993
- 16 What's wrong with this temptation, June 1994
- 17 What's wrong with this sustaining myth, March 1996
- 18 The golemization of relativity, April 1996
- 19 Diary of a Nobel guest, March 1997
- 20 What's wrong with this reading, October 1997
- 21 How not to create tigers, August 1999
- 22 What's wrong with this elegance, March 2000
- 23 The contemplation of quantum computation, July 2000
- 24 What's wrong with these questions, February 2001
- 25 What's wrong with this quantum world, February 2004
- 26 Could Feynman have said this? May 2004
- 27 My life with Einstein, December 2005
- 28 What has quantum mechanics to do with factoring? April 2007
- 29 Some curious facts about quantum factoring, October 2007
- 30 What's bad about this habit, May 2009
- Part Two Shedding Bad Habits
- Part Three More from Professor Mozart
- Part Four More to be Said
- Part Five Some People I've Known
- Part Six Summing it Up
- Index
Summary
The subject of Einstein–Podolsky–Rosen correlations—those strong quantum correlations that seem to imply “spooky actions at a distance”—has just been given a new and beautiful twist. Daniel Greenberger, Michael Horne, and Anton Zeilinger have found a clever and powerful extension of the two-particle EPR experiment to gedanken decays that produce more than two particles [1]. In the GHZ experiment the spookiness assumes an even more vivid form than it acquired in John Bell's celebrated analysis of the EPR experiment, given over 25 years ago [2]. The argument that follows is my attempt to simplify a refinement of the GHZ argument given by the philosophers Robert Clifton, Michael Redhead, and Jeremy Butterfield [3].
Consider three spin-½ particles, named 1, 2, and 3. They have originated in a spin-conserving gedanken decay and are now gedanken flying apart along three different straight lines in the horizontal plane. (It's not essential for the gedanken trajectories to be coplanar, but it makes it easier to describe the rest of the geometry.) I specify the spin state |Ψ〉 of the three particles in a time-honored manner, giving you a complete set of commuting Hermitian spin-space operators of which |Ψ〉 is an eigenstate.
Those operators are assembled out of the following pieces (measuring all spins in units of ½ ħ): σzi the operator for the spin of particle i along its direction of motion; σxi the spin along the vertical direction; and σyi, the spin along the horizontal direction orthogonal to the trajectory. (Any three orthogonal directions independently chosen for each particle would do. But we're going to be gedanken-measuring x and y components of each particle's spin, so it's nice to think of the x and y directions as orthogonal to the direction of motion, since the components can then be straightforwardly measured by passage through a conventional Stern–Gerlach magnet.) The complete set of commuting Hermitian operators consists of
σx1σy2σy3, σy1σx2σy3, σy1σy2σx3.
Even though the x and y components of a given particle's spin anticommute—a fact of paramount importance in what follows—all three of the operators in (1) do indeed commute with one another, because the product of any two of them differs from the product in the reverse order by an even number of such anticommutations. Because they all commute, the three operators can be provided with simultaneous eigenstates.
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- Why Quark Rhymes with PorkAnd Other Scientific Diversions, pp. 43 - 49Publisher: Cambridge University PressPrint publication year: 2016