Eckard,
I don't know how Peter Lynds entered this discussion. Did I miss something? I wouldn't have anything to say about that paper anyway, since I find it philosophical, and empty of scientific content.
On this petition re the twin paradox (which is not really a paradox)it sounds like an updated version of "100 scientists against Einstein." As much nonsense as it ever was.
In any case, it is quite obvious from the description of the problem that the difference between a state of uniform motion (stay at home twin & special relativity) and accelerated motion (traveling twin & general relativity) is time-asymmetric. Because classical physics is time-symmetric, it is impossible for the twins to age at the same rate from an objective point of view, though from their own inertial frames, each will see the other age more slowly. The traveling twin who reverses trajectory to return home does not instaneously age upon negative acceleration to zero -- and when positively accelerating once more in the direction of his brother, he will witness from this new inertial frame a radical curving of spacetime. Here's why:
Explaining the phenomenon in geometric terms alone (a 2 dimension analogy to a 4 dimension event) -- picture two antipodal points on a circle. Assume one to be a fixed point (stay at home twin) and the other the traveling twin. The straight line between them is oriented from the fixed point toward the opposite point, so the radius of the circle is expanding in proportion to the rate of acceleration. Nevertheless, so long as the poles remain in this fixed relation, each twin sees the other as growing older; spacetime between them is symmetric. When the traveling twin reverses course, however, the symmetry is broken -- the radius of the circle is now fixed, and the traveling twin is accelerating on the curve toward the fixed point. The intervals between the traveling twin and the stay at home twin smoothly vary in accordance with the rate of acceleration, the radius of the circle shrinking incrementally toward shorter and shorter intervals, until the points meet at zero curvature.
The aging differential is the result of the behavior of time, not space by itself. The point set geometry is indfiferent to aging, but because we know experimentally that faster moving particles are longer lived and that all motion is relative, a fixed mass, i.e., one at rest relative to a moving mass, necessarily ages faster relative to the one in motion. As a result, spacetime is a real physical phenomenon; i.e., the increments of changing relations between mass points on a curve represented by Riemannian spacetime geometry correspond to real physical processes.
However one's intuition may be scandalized by the facts, the physics is quite straightforward.
Tom