Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that models can help student understanding of special relativity and distinguishing between dynamical and purely perspectival effects.
REFERENCES
1.
Albert
Einstein
, “What is the theory of relativity?
,” reprinted in Ideas and Opinions
(Crown
, New York
, 1982
), pp. 227
–232
.2.
Harvey R.
Brown
, Physical Relativity. Space-Time Structure from a Dynamical Perspective
(Oxford U. P.
, Oxford
, 2005
).3.
Michel
Janssen
, “Drawing the line between kinematics and dynamics in special relativity
,” Stud. Hist. Philos. Mod. Phys.
40
(1
), 26
–52
(2009
).4.
John D.
Norton
, “Why constructive relativity fails
,” Br. J. Philos. Sci.
59
(4
), 821
–834
(2008
).5.
N.
David Mermin
, It’s About Time. Understanding Einstein’s Relativity
(Princeton U. P.
, Princeton
, 2005
), pp. 179
–186
.6.
John S.
Bell
, “How to teach special relativity
,” reprinted in Speakable and Unspeakable in Quantum Mechanics
, 2nd ed. (Cambridge U. P.
, Cambridge
, 2004
), pp. 67
–80
.7.
Hans C.
Ohanion
, Einstein’s Mistakes. The Human Failings of Genius
(Norton
, New York
, 2008
), p. 283
.8.
9.
M. D.
Simon
, L. O.
Heflinger
, and A. K.
Geim
, “Diamagnetically stabilized magnet levitation
,” Am. J. Phys.
69
(6
), 702
–713
(2001
).10.
William T.
Scott
, “Who was Earnshaw?
,” Am. J. Phys.
27
(6
), 418
–419
(1959
).11.
W. F. G.
Swann
, “Relativity, the Fitzgerald–Lorentz contraction and quantum theory
,” Rev. Mod. Phys.
13
(3
), 197
–202
(1941
).12.
Edwin F.
Taylor
and John Archibald
Wheeler
, Spacetime Physics
, 2nd ed. (Freeman
, New York
, 1992
), pp. 65
–67
.13.
Valery P.
Dmitriyev
, “The easiest way to the Heaviside ellipsoid
,” Am. J. Phys.
70
(7
), 717
–718
(2002
).14.
Ben Yu-Kuang
Hu
, “Comment on ‘The easiest way to the Heaviside ellipsoid’ by Valery P. Dmitriyev
,” Am. J. Phys.
71
(3
), 281
(2003
).15.
David J.
Griffiths
, Introduction to Electrodynamics
, 2nd ed. (Prentice-Hall
, Englewood Cliffs, NJ
, 1989
), pp. 425
–426
.16.
17.
In deriving Eq. (7), it has been assumed that the speed of with respect to is . This result follows from the method of clock synchronization we have assumed. It is less desirable to rely on the principle of reciprocity, which requires attributing some properties to space and time that are best to avoid in a constructive approach to special relativity.
18.
Sometimes the invariance of the speed of light for all inertial observers is made one of the two postulates in a presentation of special theory of relativity, but that is not the minimalist form of the postulates as originally proposed by Einstein.
19.
William C.
Davidon
, “Kinematics and dynamics of elastic rods
,” Am. J. Phys.
43
(8
), 705
–713
(1975
).20.
E.
Dewan
and M.
Beran
, “Note on stress effects due to relativistic contraction
,” Am. J. Phys.
27
(7
), 517
–518
(1959
).21.
The acceleration could be achieved by immersing the apparatus in a uniform gravitational field for the required period of time (a gravitational field in which tidal effects are negligible over the dimensions of the apparatus).
22.
We consider only inertial observers whose relative velocity lies along the -axis.
23.
E. L.
Feĭnberg
, “Can the relativistic change in the scales of length and time be considered the result of the action of certain forces?
,” Sov. Phys. Usp.
18
(8
), 624
–635
(1975
).24.
Wolfgang
Rindler
, Relativity. Special, General, and Cosmological
, 2nd ed. (Oxford U. P.
, Oxford
, 2006
), pp. 71
–73
.25.
26.
Alberto A.
Martinez
, “There’s no pain in the Fitzgerald contraction, is there?
,” Stud. Hist. Philos. Mod. Phys.
38
(1
), 209
–215
(2007
).27.
In the argument here it is tacitly assumed that if all the physical fields are Lorentz invariant, then all the laws of physics involving them must be Lorentz invariant.
28.
Reference 3, p.
49
.29.
Savas
Dimopoulos
, Stuart A.
Raby
, and Frank
Wilczek
, “Unification of couplings
,” Phys. Today
44
(10
), 25
–33
(1991
).30.
Frank
Wilczek
, “Anticipating a new golden age
,” Eur. Phys. J. C
59
(2
), 185
–196
(2009
).© 2010 American Association of Physics Teachers.
2010
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.
