It is easy to construct classical two-state systems illustrating the behavior of the short-lived and long-lived neutral K mesons in the limit of CP conservation. The emulation of CP violation is more tricky, but is provided by the two-dimensional motion of a Foucault pendulum. Analogies are drawn between the pendulum and observables in neutral kaon decays. An emulation of CP and CPT violation using electric circuits is also discussed.
REFERENCES
1.
We thank N. F. Ramsey for a discussion on this point. See, e.g., J. J. Sakurai, Modern Quantum Mechanics (Addison–Wesley, Reading, MA, and Menlo Park, CA, 1994), Revised ed., p. 320.
2.
G. Baym, Lectures on Quantum Mechanics (Benjamin, New York, 1969).
3.
M.
Gell-Mann
and A.
Pais
, “Behavior of neutral particles under charge conjugation
,” Phys. Rev.
97
, 1387
–1389
(1955
).4.
J. L.
Rosner
, “Table-top time-reversal violation
,” Am. J. Phys.
64
, 982
–985
(1996
).5.
J. H.
Christenson
, J. W.
Cronin
, V. L.
Fitch
, and R.
Turlay
, “Evidence for the 2π decay of the meson
,” Phys. Rev. Lett.
13
, 138
–140
(1964
).6.
B. Winstein, “CP violation,” in Festi-Val – Festschrift for Val Telegdi, edited by K. Winter (Elsevier, Amsterdam, 1988), pp. 245–265.
7.
H. Goldstein, Classical Mechanics (Addison–Wesley, New York, 1980), 2nd ed., p. 177.
8.
G. D.
Rochester
and C. C.
Butler
, “Evidence for the existence of new unstable elementary particles
,” Nature (London)
160
, 855
–857
(1947
).9.
M.
Gell-Mann
, “Isotopic spin and new unstable particles
,” Phys. Rev.
92
, 833
–834
(1953
);“On the Classification of Particles,” 1953 (unpublished);
M. Gell-Mann and A. Pais, in Proceedings of the 1954 Glasgow Conference on Nuclear and Meson Physics, edited by E. H. Bellamy and R. G. Moorhouse (Pergamon, London and New York, 1955);
M.
Gell-Mann
, “The interpretation of the new particles as displaced charge multiplets
,” Nuovo Cimento Suppl.
4
, 848
–866
(1956
);T.
Nakano
and K.
Nishijima
, “Charge independence for-particles
,” Prog. Theor. Phys.
10
, 581
–582
(1953
);K.
Nishijima
, “Some remarks on the even–odd rule
,” Prog. Theor. Phys.
12
, 107
–108
(1954
);K.
Nishijima
, “Charge independence theory of -particles
,” Prog. Theor. Phys.
13
, 285
–304
(1955
).10.
K.
Lande
, E. T.
Booth
, J.
Impeduglia
, and L. M.
Lederman
, “Observation of long-lived -particles
,” Phys. Rev.
103
, 1901
–1904
(1956
).11.
See, e.g., R. G. Sachs, The Physics of Time Reversal Invariance (University of Chicago Press, Chicago, 1988).
12.
J.
Schwinger
, “The theory of quantized fields. II
,” Phys. Rev.
91
, 713
–728
(1953
) (see especially p. 720 ff);J.
Schwinger
, “The theory of quantized fields. VI
,” Phys. Rev.
94
, 1362
–1384
(1954
) [see especially Eq. (54) on p. 1366 and p. 1376 ff];G.
Lüders
, “On the equivalence of invariance under time reversal and under particle-antiparticle conjugation for relativistic field theories
,” Kong. Danske Vid. Selsk., Matt-fys. Medd.
28
(5
), 1
–17
(1954
);“
G.
Lüders
, Proof of theTCP theorem
,” Ann. Phys. (N.Y.)
2
, 1
–15
(1957
);W. Pauli, in “Exclusion principle, Lorentz group, and reflection of space-time and charge,” Niels Bohr and the Development of Physics (Pergamon, New York, 1955), pp. 30–51.
13.
Particle Data Group,
C.
Caso
et al., “Review of particle physics
,” Eur. Phys. J. C
3
, 1
–794
(1998
).14.
T. P. Cheng and L. F. Li, Gauge Theory of Elementary Particles (Oxford U.P., Oxford, 1984);
K. Kleinknecht, “CP violation in the system,” in CP Violation, edited by C. Jarlskog (World Scientific, Singapore, 1989), pp. 41–104;
B.
Winstein
and L.
Wolfenstein
, “The search for directCP violation
,” Rev. Mod. Phys.
63
, 1113
–1148
(1992
);P. K. Kabir, The CP Puzzle (Academic, New York, 1968).
15.
L.
Wolfenstein
, “Violation of CP invariance and the possibility of very weak interactions
,” Phys. Rev. Lett.
13
, 562
–564
(1964
).16.
N.
Cabibbo
, “Unitary symmetry and leptonic decays
,” Phys. Rev. Lett.
10
, 531
–532
(1963
);M.
Kobayashi
and T.
Maskawa
, “CP violation in the renormalizable theory of the weak interaction
,” Prog. Theor. Phys.
49
, 652
–657
(1973
).17.
R. H. Dalitz, “Kaon physics—The first 50+ years,” in Kaon Physics, edited by J. L. Rosner and B. Winstein (University of Chicago Press, Chicago, to be published).
18.
P. K.
Kabir
, “What is not invariant under time reversal?
,” Phys. Rev. D
2
, 540
–542
(1970
).19.
CPLEAR Collaboration
, A.
Angelopoulos
et al., “First observation of time reversal noninvariance in the neutral kaon system
,” Phys. Lett. B
444
, 43
–51
(1998
).
This content is only available via PDF.
© 2001 American Association of Physics Teachers.
2001
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.