A novel graphical depiction of the relativistic barn and pole paradox is constructed in such a way that the space-time plot axes are dimensionless for both observers. Times of events over the entire range of pole-to-barn length ratio and relative speeds can be displayed in one plot for each observer. That for the barn frame clearly depicts the range of pole-to-barn length ratio over which the paradox appears, while that for the pole frame shows that the pole vaulter will only see the pole within the barn if the proper length of the pole is smaller than the contracted length of the barn.
REFERENCES
1.
W.
Rindler
, “
Length contraction paradox
,” Am. J. Phys.
29
(6
), 365
–366
(1961
);W.
Rindler
, “
Erratum
,” Am. J. Phys.
29
(12
), 859
(1961
).2.
W. H.
Wells
, “
Length contraction paradox
,” Am. J. Phys.
29
(12
), 858
(1961
).3.
R.
Shaw
, “
Length contraction paradox
,” Am. J. Phys.
30
(1
), 72
(1962
).4.
E. M.
Dewan
, “
Stress effects due to Lorentz contraction
,” Am. J. Phys.
31
(5
), 383
–386
(1963
).5.
E.
Marx
, “
Lorentz contraction
,” Am. J. Phys.
35
(12
), 1127
–1130
(1967
).6.
R. de A.
Martins
, “
Length paradox in relativity
,” Am. J. Phys.
46
(6
), 667
–670
(1978
).7.
G. P.
Sastry
, “
Is length contraction really paradoxical?
,” Am. J. Phys.
55
(10
), 943
–946
(1987
).8.
H.
van Lintel
and
C.
Gruber
, “
The rod and hole paradox re-examined
,” Eur. J. Phys.
26
(1
), 19
–23
(2005
).9.
R.
Knight
, Physics for Scientists and Engineers: A Strategic Approach
, 4th ed. (
Pearson
,
London
, 2017
), problem 36
–77
.10.
J.
Walker
, Fundamentals of Physics
, 10th ed. extended (
Wiley
,
Hoboken, NJ
, 2014
), problem 37
–69
.11.
12.
E. F.
Taylor
and
J. A.
Wheeler
, Spacetime Physics
, 2nd ed. (
Freeman
,
New York
, 1992
), p. 166
.13.
R.
Sexl
and
H.
Urbantke
, Relativity, Groups, Particles
(
Springer
,
Vienna
, 2001
).14.
A.
Lampa
, “
Wie erscheint nach der Relativitätstheorie en bewegter Stab einem ruhenden Beobachter?
,” Z. Phys.
27
(11
), 138
–148
(1924
).15.
R.
Penrose
, “
The apparent shape of a relativistically moving sphere
,” Math. Proc. Camb. Philos. Soc.
55
(1
), 137
–139
(1959
).16.
J.
Terrel
, “
Invisibility of the Lorentz contraction
,” Phys. Rev.
116
(4
), 1041
–1045
(1959
).17.
R.
Weinstein
, “
Observation of length by a single observer
,” Am. J. Phys.
28
(7
), 607
–610
(1960
).18.
G. D.
Scott
and
M. R.
Viner
, “
The geometrical appearance of large objects moving at relativistic speeds
,” Am. J. Phys.
33
(7
), 534
–536
(1965
).© 2021 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2021
Author(s)
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.