The frequently used analogy of a massive ball distorting an elastic sheet, which is used to illustrate why mass causes spacetime curvature and gravitational attraction, is criticized in this article. A different analogy that draws on the students’ previous knowledge of spacetime diagrams in special relativity is suggested.

1.
See, for example,
A.
Pais
, “Subtle is the Lord–”;
The Science and the Life of Albert Einstein
(
Oxford
,
1982
), p.
253
.
2.
Many years later, Einstein and collaborators showed that the equations of motion were actually consequences of the field equations. See, for example,
A.
Einstein
,
L.
Infeld
, and
B.
Hoffmann
, “
The gravitational equations and the problem of motion
,”
Ann. Math.
39
,
65
100
(
1938
).
3.
See, for example,
C. W.
Misner
 et al,
Gravitation
(
Freeman
,
1973
), p.
32
. They show a diagram similar to Fig. 1, but the picture caption makes clear that they are aware of its shortcomings. The textbook Gravity by E. Poisson and C. Will (Cambridge, 2014) features a similar picture on its cover.
4.
The scarcity of hands-on demonstrations of general relativistic concepts undoubtedly contributes to the appeal of this analogy in spite of its shortcomings. Note that this analogy has been examined in detail in
C.
Middleton
and
M.
Langston
, “
Circular orbits on a warped spandex fabric
,”
Am. J. Phys.
82
,
287
294
(
April
2014
).
5.
See Supplemental tab at TPT Online,https://doi.org/10.1119/1.5018679 .
6.
There is an opportunity for a classroom activity here. If a piece of string is pulled taut on an Earth globe while passing through Ottawa and Venice (or any two widely separated points at the same latitude in the Northern Hemisphere), it will be seen that the string lies north of those two points.
7.
R. H.
Price
, “
Spatial curvature, spacetime curvature, and gravity
,”
Am. J. Phys.
84
,
588
592
(
Aug.
2016
).

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