In 1964 John Bell proved a theorem2 allowing the experimental test of whether what Einstein derided as “spooky actions at a distance” actually exist. We will see that they do. Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at any level. And a simple, semi‐classical derivation of the quantum theory result can be given for physics students. These entanglement phenomena are today applied in industrial laboratories and are increasingly discussed in the popular literature. Unfortunately, they are also misappropriated by the purveyors of pseudoscience, something physicists have a responsibility to address.3 Students can be intrigued by the quantum strangeness physics has encountered at a boundary of our discipline.

Topics
Thought experiments, Flavour quantum numbers, Educational assessment, Bell's theorem, Quantum entanglement, Quantum mechanics, Quantum theory, Physicists, Laboratories
1.
Parts of this article have been taken from the revised paperback edition of our book, Quantum Enigma: Physics Encounters Consciousness, with the permission of Oxford University Press.
2.
J. S. Bell, “On the Einstein‐Rosen‐Podolsky paradox,” in Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, New York, 1987), pp. 14–21.
3.
F.
Kuttner
 and
B.
Rosenblum
, “
Teaching physics mysteries versus pseudo‐science
,”
Phys. Today
59
(
11
),
14
–
16
(Nov.
2006
).
Google Scholar
Crossref
Search ADS
 
4.
A.
Einstein
,
B.
Podolsky
, and
N.
Rosen
, “
Can quantum‐mechanical description of physical reality be considered complete?
”
Phys. Rev.
47
,
777
–
780
(May
1935
).
Google Scholar
Crossref
Search ADS
 
5.
D. J. Griffiths, Introduction to Quantum Mechanics (Prentice‐Hall, Englewood Cliffs, NJ, 1995), p. 3.
6.
D. Bohm, Quantum Theory (Prentice‐Hall, New York, 1951), pp. 611–622.
7.
The two photons are together in a singlet state: ψ = (| x> | x> − | y> | y>)/√2.
8.
R. L. Liboff, Introductory Quantum Mechanics, 2nd ed. (Addison‐Wesley, Reading, MA, 1992), pp. 546–553.
9.
N.
Herbert
, “
Cryptographic approach to hidden variables
,”
Am. J. Phys.
43
(
4
),
315
–
316
(April
1975
).
Google Scholar
Crossref
Search ADS
 
10.
S. J.
Freedman
 and
J. F.
Clauser
, “
Experimental test of local hidden‐variable theories
,”
Phys. Rev. Lett.
28
,
938
–
941
(April
1972
).
Google Scholar
Crossref
Search ADS
 
11.
This is Malus' law treated in most introductory texts. For example, R. Wolfson, Essential University Physics (Addison‐Wesley, San Francisco, 2007), p. 518.
12.
A.
Aspect
,
J.
Dalibard
, and
G.
Roger
, “
Experimental test of Bell's inequalities using time‐varying analyzers
,”
Phys. Rev. Lett.
49
(
25
),
1804
–
1807
(Dec.
1982
).
Google Scholar
Crossref
Search ADS
 
13.
This point is dramatically made by
D. Z.
Albert
 and
R.
Galchen
, “
Was Einstein wrong?: A quantum threat to special relativity
,”
Sci. Am.
300
(
3
),
32
–
39
(March
2009
).
Google Scholar
Crossref
Search ADS
PubMed
 
14.
M.
Ansmann
 et al., “
Violation of Bell's inequality in Josephson phase qubits
,”
Nature
461
,
504
–
506
(Sept. 24,
2009
).
Google Scholar
Crossref
Search ADS
PubMed
 
15.
J. S. Bell, “Bertlmann's socks and the nature of reality,” in Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, New York, 1987), p. 154. The conflict between the perception of “freely operating experimenters” and the experimental data is more strikingly seen in a theory‐neutral version of the two‐slit experiment in B. Rosenblum and F. Kuttner, Quantum Enigma: Physics Encounters Consciousness (Oxford University Press, New York, 2008), Chap. 9; online at http://www.quantumenigma.com/nutshell/.
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