Institute for Problems in Mechanics, Russian
Academy of Sciences
101-1 ,Vernadskii Ave., Moscow, 119526, Russia
Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
or mirror Web site: http://gas-dyn.ipmnet.ru/~rylov/yrylov.htm
Updated January, 21, 2013
It is shown that the space-time geometry should be formulated in terms of the world function, because only description in terms of world function admits one to recognize similar geometrical objects in regions of the space-time geometry with different geometries. The Berwald-Moor geometry formulated in terms of the world function appears to be multivariant geometry, which hardly can be used as a space-time geometry, because in this geometry the world lines wobbling of free particles differs from the real wobbling.