W.D.Clinger
Philosopher
Irrelevant. Eddington was talking about empty space, "independent of matter". As can be seen from de Sitter's space, lambda acts to expand even empty spacetime, devoid of matter.
Its physical implications are consequences of its mathematical meaning, which is the meaning of the "stretching" itself. To give just one example, consider two particles separated by an expanse of empty space, and suppose the two particles start out at rest with respect to each other. That's means their world lines start out parallel. If the space between them expands, they will not only become farther apart but their world lines will no longer be parallel. Suppose further that the two particles have agreed to communicate via a certain radio frequency. The photons sent between them will be red-shifted, so they'll have to tune their receivers to a lower frequency than their transmitters. Et cetera.
What's making it stretch? That's a little more philosophical. I'd say the space-time manifold is itself the source of the stretch. You want physics? The manifold itself is constrained, but seldom determined, by physical laws. In other words, the physical laws say what can happen and what can't happen, but don't always tell you what will happen. That's physics, and that's science in general. Deal with it.
So say you.
Einstein, however, says the stress-energy-momentum tensorWP is defined by other physics, and his field equations describe how space-time (including empty space!) must be compatible with that tensor.
