I consider two identical quantum particles in two boxes. We can split each box and thereby the wavefunction of each particle into two parts. When two half boxes are interchanged and combined with the other halves, where are the two particles? I solve this problem for two identical bosons and for two identical fermions. The solution can be used to define a measurement that yields some information about the relative phase between the two parts of a split wavefunction.

1.
A.
Einstein
,
B.
Podolski
, and
N.
Rosen
, “
Can quantum mechanical description of physical reality be considered complete?
,”
Phys. Rev.
47
,
777
780
(
1935
).
2.
T.
Norsen
, “
Einstein’s boxes
,”
Am. J. Phys.
73
,
164
176
(
2004
).
See also
A.
Shimony
, “
Comment on Norsen’s defense of Einstein’s ‘box argument
,’”
Am. J. Phys.
73
,
177
178
(
2005
).
3.
J.
Gea-Banacloche
, “
Splitting the wavefunction of a particle in a box
,”
Am. J. Phys.
70
,
307
312
(
2002
).
4.

In an informal poll among 14 scientists present at a meeting at the Perimeter Institute, Waterloo, Canada, in June 2008, the voting distribution for answers 1–4 was 2, 2, 4, 2, respectively, with four choosing the fifth answer “I don’t know.”

5.
C. K.
Hong
,
Z. Y.
Ou
, and
L.
Mandel
, “
Measurement of subpicosecond time intervals between two photons by interference
,”
Phys. Rev. Lett.
59
,
2044
2046
(
1987
).
6.
M.
Lakner
and
J.
Peternelj
, “
Comment on ‘Splitting the wavefunction of a particle in a box
,’”
Am. J. Phys.
71
,
519
(
2003
).
7.
Y.
Aharonov
and
L.
Vaidman
, “
Nonlocal aspects of a quantum wave
,”
Phys. Rev. A
61
,
052108
1
(
2000
).
8.
S. D.
Bartlett
,
T.
Rudolph
, and
R. W.
Spekkens
, “
Reference frames, superselection rules, and quantum information
,”
Rev. Mod. Phys.
79
,
555
610
(
2007
).
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