woodysooner said:
oh, and what is the metric field... sorry if I am lil dumb in this. is that something to do with tensors or at least i always think i see that in discussions on tensors.
still not sure what a tensor is, went to john baez's site(absolutely kewl) to learn more bout einsteins equation and tensors, but still not getting it so if you or anyone can give me an idea it would be appreciated greatly.
A tensor is not such a mysterious thing. Consider a vector : it is quantity that carry one indice : in the usual 3-dim space, the indice runs over x, y and z. Denote V_i the vector. The vectorial nature can be expressed by the fact that when one changes the basis in space, the new value of the coordinate of the vector are determined by a linear combination of the old values :
V_{j(new)} = \sum_i O_{i,j} V_{i(old)}
Here, O_{i,j} is a matrix related to the change of basis.
Now a tensor carries several indices : for example with two indices, one gets
T_{k,l} = O_{i,k} O_{l,j} T_{i,j}
with an implicit sum over i and j
This is one way to define tensor : through their transformation law. One can also use other equivalent definitions, depending on what feature one wants to inlight. The definition given here is not very geometric for instance.
The metric tensor allows one to compute infinitesimal length in spacetime. The length of the very small intervall with coordinates V_i is given by :
\textquotedblright length\textquotedblright = \sqrt{ g_{i,j} V_i V_j }
between quotes because this is not the usual euclidian length.
In flat spacetime, one can find a basis in which the metric is diagonal and given by :
\textquotedblright length\textquotedblright = \sqrt{ t^2 -x^2-y^2-z^2 }
Diagonal means that there is no such term as x\times y for instance.
You see that it vanishes along a path taken by light rays. Maybe now you could say "the metric field is a rank two tensor". It is symmetric. (Is it obvious ?) This in turn implies that the graviton has spin 2.
