Re: What causes my spring to stretch?

hi Paul,

your question is a very interesting one and a not a really solved one. In fact we do not know whether your spring will stretched or not, when the universe (that means, all the masses of the universe except the two cannon balls and the spring between them) is rotating around them. Experiments like that cannot be performed.

Your question is all about something Einstein called "Mach's Principle" after the Austrian physicist Ernst Mach.

So let us begin with Newton. Newton abstracts from space and time which is given to our perception and talks about absolute space and absolute time. Inertial forces (e.g. centrifugal force) do not occur if you describe all the motions relative to absolute space. Therefore Newton would say that the masses of the universe spinning around the cannon balls would have no effect on the spring at all! since the cannon balls are not moving relative to absolute space. Relative motion to ABSOLUTE SPACE is relevant.

Mach has a different way of thinking. He rejects the concept of absolute space and absolute time. He says that we can only measure motion, change, time comparing it to some reference motion, for example the spinning the earth. A particle's motion is uniform, if the particle goes equal distancies while a reference motion goes also equal distancies. So instead of absolute space Mach uses some average over the universe's mass distribution (fixed stars) as reference system. Relative motion to the FIXED STARS is relevant.

Mach thinks that inertia (and inertial forces such as the centrifugal force) of a particle is due to gravitational interaction of that particle with all other masses in the universe. If the universe was empty except of one particle, you would not be ablbe to talk about its mass.

In our example of the cannon balls joined by a spring, the relative motion is the same in both cases, no matter whether the fixed stars rotate around the cannon balls or whether the cannon balls spin about each other. Therefore also the effect is the same, the spring is stretched. Mach would answer your question, What causes my spring to stretch? : it's the gravitational interaction with the fixed stars - in both cases. (cf. Wolfgang Rindler, Essential Relativity)

Einstein was inspired by Mach's principle and wanted to build it into his theory of general relativity, which he did not really succeed in. Einstein has abolished absolute space, but instead of explaining inertial forces as gravitational, he explains gravitational forces as inertial. Some solutions to the Einstein field equations have been found that violate Mach's principle (see again Rindler for a reference).

I hope this helps,
Michael