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## Main Question or Discussion Point

Here are two seemingly unrelated arguments to explain why GR is a nonlinear theory:

(1) By the equivalence principle, any form of mass-energy should cause gravitational fields. Since gravitational fields carry energy, they should cause gravitational fields.

(2) GR doesn't care what coordinates we use. Therefore there is no natural way to identify the points of one spacetime with the points of another. This means that we can't add two metrics in any natural way.

I think #1 is pretty standard. #2 is raised by more than one author in Callender 2001. It's an anthology about quantum gravity, but this particular argument seems to me to apply just as well to classical superposition as to quantum-mechanical superposition.

I haven't seen #2 applied to classical GR before. Am I correct to do so? Is either 1 or 2 more fundamental? They seem unrelated; is there any connection I'm missing?

Craig Callender and Nick Huggett, eds., Physics Meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity, 2001.

(1) By the equivalence principle, any form of mass-energy should cause gravitational fields. Since gravitational fields carry energy, they should cause gravitational fields.

(2) GR doesn't care what coordinates we use. Therefore there is no natural way to identify the points of one spacetime with the points of another. This means that we can't add two metrics in any natural way.

I think #1 is pretty standard. #2 is raised by more than one author in Callender 2001. It's an anthology about quantum gravity, but this particular argument seems to me to apply just as well to classical superposition as to quantum-mechanical superposition.

I haven't seen #2 applied to classical GR before. Am I correct to do so? Is either 1 or 2 more fundamental? They seem unrelated; is there any connection I'm missing?

Craig Callender and Nick Huggett, eds., Physics Meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity, 2001.