A new theory of gravitation is developed. The theory is equivalent to that of Einstein in the description of macroscopic phenomena, and hence the situation is the same so far as the classical tests of general relativity are concerned. The new theory differs in its global implications, however. There are two main differences of principle. In the usual theory, the negative sign of the constant of proportionality –8
πG
which appears in the field equations
R
ik
– ½
g
ik
R
= –8
πGT
ik
is chosen arbitrarily. In the present theory there is no such ambiguity; the sign must be minus. Further, the magnitude of
G
follows from a determination of the mean density of matter, thereby enabling the cosmologist to know how hard he will hit the ground if he is unfortunate enough to fall over a cliff. The second point of principle is that the equation
R
ik
= 0 for an empty world in Einstein theory becomes meaningless; there is no such thing as an ‘empty’ world; in the present theory emptiness demands no world at all. Nor can there be a world containing a single particle, the least number of particles is two.
Centrifugal (centripetal) and Coriolis' velocities and accelerations in $$ (\bar L_n ,g) $$ -spaces