[ajkjk]

The argument presupposes that a person either believes (if they're not a physicist) or knows (if they are) that a spin-2 field must obey those rules, and that gravity is a spin-2 field, which makes the conclusion follow naturally.

The math for this would not make any sense to a layperson, but is widely accepted. Proposing a new theory of negative mass means proposing much more significant alterations to the underlying theory of gravity; the theoretical machinery supporting this current understanding is huge.

[eutropia]

True. I'm not a physicist, so help me understand -- we've only ever observed fermions with spin 1/2 and bosons with spin 1 (and recently, Higgs at 0). We've postulated that gravitons would have to be spin-2 because of how the math works out (I don't understand the math but wikipedia suggests that its because gravity is defined by the use of 2nd order tensors) but we've not confirmed the existence of gravitons. Hopefully I'm not talking past you by speaking of particles, correct me if I'm wrong but particles/fields are interchangeable as a matter of quantization, right?

I definitely trust the general relativity math -- gravitational lensing /GPS atomic clock corrections are perhaps the easiest bits to wrap my head around as evidence.

Anyways, all that is to ask the question -- Is this negative mass model in conflict with observations or is it in conflict with other models of those observations?

[ajkjk]

I am not an expert on this either, though I guess I hope to be someday. But when Hossenfelder says that Spin-2 necessitates like charges attracting, I believe her. I've also heard that result elsewhere.

My understanding is that the spin of a field or particle is more of a result of the equation (specifically, the Lagrangian) which governs its dynamics. This is irrespective of whether you consider it as a field or as a quantized particle of that field; either way the Lagrangian has certain symmetries. The Fermion Lagrangian has symmetry on 4pi rotation, but not 2pi, which (confusingly) we call spin-1/2. I suppose that the GR Lagrangian has symmetry under pi rotations, which corresponds to spin-2.

(that would make sense if the stress-energy tensor is contracted with two vectors; it would essentially boil down to the fact that (-x^T) M (-x) = x^T M x if you wrote everything as matrices. But while I have studied GR I haven't studied it as a field theory so I'm not sure it's this simple.)

So the Spin-2 thing is not too questionable. I don't anything about how to turn that into a statement about gravitational charges, though.