8.2 Other choices for physical identification
The question of whether our definition of the complex center of mass is the best possible definition, or
even a reasonable one, is not easy to answer. We did try to establish a criteria for choosing such a definition:
(i) it should predict already known physical laws or reasonable new laws, (ii) it should have a clear
geometric foundation and a logical consistency and (iii) it should agree with special cases, mainly
the algebraically-special metrics or analogies with flat-space Maxwell theory. We did try out
several other possible choices [42
] and found them all failing. This clearly does not rule out
others that we did not think of, but at the present our choice appears to be both natural and
effective in making contact with physical phenomena. There still remains the mystery of the
physical meaning of
-space or why it leads to such reasonable physical results. Possible
resolutions appear to lie in the duality between the complex world lines and real but twisting
NGCs [8].