GR and the role of the graviton

Fredrik

Why is it not a tensor? To me it looks like all three quantities are defined as tensors.

Mentz114

I'm not so sure now but I do know that for g_mn to be a covariant tensor, then under transformation from [itex]x^\mu[/itex] to [itex]x^\bar{\mu}[/itex]
[tex]g_{\bar{m}\bar{n}}=g_{mn}A^n_{\bar{n}}A^m_{\bar{m}}[/tex]
where
[tex]A^n_{\bar{n}}=\frac{\partial x^n}{\partial x^\bar{n}}[/tex]

I don't think [itex]\eta_{mn}+h_{mn}[/itex] satisfies this rule.

I could be wrong, maybe someone can clarify ?

jnorman

in my view, quantum gravity (ie, gravitational force as a result of the interaction of graviton particles with other particles) is a non-starter. there is no conceivable mechanism by which particle interaction could result in the perfectly smooth "bending" of light as it passes a massive star.

Fredrik

I just assumed that the separation of g into two pieces is done like this: You start with a quantity g, which is assumed to be a tensor. Then you just express it as [itex]g=\eta+g-\eta[/itex] where [itex]\eta[/itex] is defined as the tensor that has components [itex]\eta_{\mu\nu}[/itex] in some coordinate system. That makes sure that both [itex]\eta[/itex] and [itex]h[/itex] are tensors.

It's a bit strange that we have to mention a coordinate system. There will be issues to deal with, like "In what coordinate systems are the components of [itex]\eta[/itex] equal to [itex]\eta_{\mu\nu}[/itex]?". I don't know anything about how those issues were dealt with. It's been about 10 years since that time when I took a quick look at an old article where they did these things. I never tried to really understand it.

Naty1

Fredrik: You are being watched!!!!

jnorman : Harsh assessment..you just killed all of string theory....