> If gravity wasn't self interacting it wouldn't follow the shortest path that gravity itself creates.
I don't know if this is the right way to think about this. Gravity follows all paths. In a sense, it is the path. Or, as Hawking described it[0]:
> [Gravity] shapes the arena in which it acts, unlike other fields which act in a fixed spacetime
background.
Back to your comment:
> So gravity is almost certainly self interacting.
I'm confused by the "almost certainly". I think this has long been established[1], but for entirely different reasons: The Einstein field equations are highly non-linear, so of course there will be self-interaction.
Or, if you prefer to think of the Einstein-Hilbert action: The Lagrangian density L = R · sqrt(det|g|) behaves as L ~ g⁻¹ · Ric · g², and the Ricci tensor is Ric ~ (∂g)∂(g⁻¹) + g⁻¹ ∂²g + (g⁻¹)²(∂g)², so if we view gravity as a quantum field theory (effective or whatever), there are plenty of self-interaction terms that will prevent the N-point function from vanishing for N > 2. Already in the weak field approach (where you approximate g = 1 + h) you get a triple graviton vertex, see p. 21 of https://arxiv.org/abs/1702.00319 .
Maybe we are talking about different definitions of "self-interaction here"?
I don't know if this is the right way to think about this. Gravity follows all paths. In a sense, it is the path. Or, as Hawking described it[0]:
> [Gravity] shapes the arena in which it acts, unlike other fields which act in a fixed spacetime background.
Back to your comment:
> So gravity is almost certainly self interacting.
I'm confused by the "almost certainly". I think this has long been established[1], but for entirely different reasons: The Einstein field equations are highly non-linear, so of course there will be self-interaction.
Or, if you prefer to think of the Einstein-Hilbert action: The Lagrangian density L = R · sqrt(det|g|) behaves as L ~ g⁻¹ · Ric · g², and the Ricci tensor is Ric ~ (∂g)∂(g⁻¹) + g⁻¹ ∂²g + (g⁻¹)²(∂g)², so if we view gravity as a quantum field theory (effective or whatever), there are plenty of self-interaction terms that will prevent the N-point function from vanishing for N > 2. Already in the weak field approach (where you approximate g = 1 + h) you get a triple graviton vertex, see p. 21 of https://arxiv.org/abs/1702.00319 .
Maybe we are talking about different definitions of "self-interaction here"?
[0]: Hawking: The Nature of Space and Time (1994), https://arxiv.org/abs/hep-th/9409195
[1]: See e.g. https://physics.stackexchange.com/questions/293873/do-gravit...