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If the metric ##g_{\mu\nu}## is dimensionless and gravitons are quantum excitations of the metric does that mean that gravitons themselves are dimensionless?

I say this as locally the metric is just the flat metric ##\eta_{\mu\nu}=\hbox{diag}(-1,1,1,1)## with the dimensions in the co-ordinates ##x^\mu##.

To put it another way:

Is graviton energy included in the stress-energy tensor ##T_{\mu\nu}##?

Actually classical gravitational waves can be detected so does that imply that gravitons can't be dimensionless?

I say this as locally the metric is just the flat metric ##\eta_{\mu\nu}=\hbox{diag}(-1,1,1,1)## with the dimensions in the co-ordinates ##x^\mu##.

To put it another way:

Is graviton energy included in the stress-energy tensor ##T_{\mu\nu}##?

Actually classical gravitational waves can be detected so does that imply that gravitons can't be dimensionless?

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