The question: What are the components of the gab metric in Kaluza-Klein theory?

[shounakbhatta]

Hello,

I am trying to understand Kaluza Klein theory on the five dimensional unification. It was mentioned over there:

" Of the 15 components of gαβ, five had to get a new physical interpretation, i.e. gα5 and g55; the components gik, i,k = 1,...,4, were to describe the gravitational field as before; Kaluza took gi5 proportional to the electromagnetic vector potential Ai"

My question is that gαβ, if I take the metric tensor of general relativity has 16 components (g00...g33). Can anybody please clarify?


Thanks

 

[Dale]

Due to symmetry only 10 of the 16 components are independent. Similarly, although adding a 5th dimension gives 9 more components, only 5 are independent.