Kaluza-Klein-Carmeli Metric from Quaternion-Cliord Space, Lorentz’s Force, and Some Observables

Abstract

It was known for quite long time that a quaternion space can be generalized to a Clifford space, and vice versa; but how to find its neat link with more convenient metric form
in the General Relativity theory, has not been explored extensively. We begin with a representation of group with non-zero quaternions to derive closed FLRW metric [1],
and from there obtains Carmeli metric, which can be extended further to become 5D and 6D metric (which we propose to call Kaluza-Klein-Carmeli metric). Thereafter
we discuss some plausible implications of this metric, beyond describing a galaxy’s spiraling motion and redshift data as these have been done by Carmeli and Hartnett
[4, 5, 6]. In subsequent section we explain Podkletnov’s rotating disc experiment. We also note possible implications to quantum gravity. Further observations are of course recommended in order to refute or verify this proposition.