Newton introduced the concept of an absolute space as a necessary ingredient
in the definition of acceleration and the interpretation and use of *F
= ma*. This is a

hard concept for many to swallow in view of the fact that we experience,
in our everyday lives, that positions and velocities are relative. Certainly
Newton was

criticized for it but the success of his program of mechanics over
the next 2½ centuries left little for critics to attack. As a practical
matter, and as the experiment of

Foucault showed, absolute space meant the space of the fixed stars.

Foucault pendulum and the fixed stars was neither an accident nor proved the existence of an absolute space but rather that the stars were responsible for the inertia

of the pendulum bob. This would eliminate Newton's absolute space which Mach viewed as metaphysical and in addition suggested a cause for mass which then

elevated it to something other than just a free parameter in Newton's theory.

Einstein was strongly influenced by Mach and the general theory of relativity
may be said to have vindicated Mach --- but only in part. Certainly we
now know that

matter influences space and there are certain model calculations which
are suggestive. For example, if a rotating shell of matter is introduced
into an otherwise empty

space, the equations of motion of test particles at the centre are
modified. In particular, an inertial frame at the centre is now a frame
that rotates at some speed that

is determined by the mass, radius and rotation speed of the shell.
(The two speeds are not equal except in a certain limit of large mass and
radius.) Thus the shell of

mass (read distant stars?) has affected the choice of "absolute space"
but it has not completely determined it as would be required by Mach in
that the mathematical

solution has used boundary conditions at infinity that are quite independent
of the matter distribution.

The problem remains an active field of research. At an elementary level
one can say the pendulum in this room shows that the earth is rotating.
But it also leaves open the more fundamental questions as to the origin
of mass and inertia. We still wonder why is there mass? why inertia? why
*F
= ma*?