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A more physical attempt: In general relativity, the metric tensor represents local clock and ruler measurments. If I multiply the metric tensor by a scalar constant, it should be obvious that this is inequivalent (in general) to a set of coordinate transformations, but, at the same time, I'm affecting local clock and ruler measurments (the ratio of the ...


General relativity is only conformally invariant in two dimensions. This can be proven by making the transformation $g_{ab} \rightarrow \phi g_{ab}$, and seeing what transformation Einstein's equation${}^{1}$ makes. What you will find is that Einstein's equation will MOSTLY transform, but you will get terms proportional to $(d-2)(d-1)$ and derivatives of ...


Newton's constant is dimensionful. Hence the theory is NOT conformally invariant. In 2 dimensions, newtons constant is dimensionless. But then the apparent conformal symmetry is actually only a REDUNDANCY in the description (sometimes called weyl symmetry).

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