Fundamental questions

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.

The debate was reopened in the latter part of the 19th century by Mach who put forward the argument that the correlation between the plane of oscillation of the
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?

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