challenged, but it has withstood all attacks for three centuries
. It has then
collapsed under Einstein’s alternative and more effective answer.
Newton needed (accelerated) motion, exempliﬁed by the rotation of the water
in the bucket, to be absolute for the foundation of his dynamics. Without this,
Newton’s main law
F ¼ m
a would not even make sense: what would be the
meaning of the acceleration
Opposition to Newton’s absolute space was very strong. Leibniz and his
school argued ﬁercely against absolute motion and absolute acceleration.
Doubts never really disappeared all along the centuries and a feeling kept lin-
gering that something was wrong with Newton’s argument. Ernst Mach re-
turned to the issue suggesting that Newton’s bucket argument could be wrong
because the water does not rotate with respect to absolute space: it rotates with
respect to the full matter content of the universe. But the immense empirical
triumph of Newtonianism could not be overcome. For three centuries.
After three centuries, Einstein found a new and simpler answer. The bending
of the surface of the water is due to the relative motion of the water with respect
to a physical entity: the local gravitational ﬁeld. It is the gravitational ﬁeld, not
Newton’s inert absolute space that tells objects if they are accelerating or not, if
they are rotating or not. There is no inert background entity such as Newtonian
space: there are only dynamical physical entities. Among these are the ﬁelds,
introduced in our physical picture of the world by Faraday and Maxwell.
Among the ﬁelds is the gravitational ﬁeld.
Whether the water surface in Newton’s bucket is concave or ﬂat is not deter-
mined by the motion of the water with respect to absolute space. It is determined
by the physical interaction between the water and the gravitational ﬁeld. Einstein’s
discovery is that Newton had mistaken the gravitational ﬁeld for absolute space.
In Newtonian physics, the spacetime coordinates
x and t refer to absolute
space. They can be identiﬁed with the reading of measuring devices carefully
selected as the ones that capture the structure of space and time. This selection is
obtained by monitoring and correcting the ‘‘inertial’’ effects such as the bending
of the water of the water, which signal motion with respect to absolute space.
Or course relationalism, i.e., the idea that motion can be deﬁned only in relation to other objects,
should not be confused with Galilean relativity. Galilean relativity is the statement that ‘‘rectilinear
uniform motion’’ is a priori indistinguishable from stasis. This is equivalent to saying that velocity
(just velocity!), is only relative to other bodies. Relationalism, on the other hand, holds that any
motion (however zigzagging) is a priori indistinguishable from stasis. The very formulation of Gali-
lean relativity assumes a nonrelational deﬁnition of motion: ‘‘rectilinear and uniform’’ with respect to
what? When Newton claimed that motion with respect to absolute space is real and physical, he, in a
sense, overdid it, by insisting that even rectilinear uniform motion is absolute. This caused a painful
debate, because there are no physical effects of inertial motion (therefore the bucket argument fails
for this particular class of motions). Newton is well aware of this point, which is clearly stated in the
Corollary V5 of the Principia, but he chooses to ignore it in the introduction of the Principia. I think
he did this just to simplify his argument, which was already hard enough for his contemporaries.