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Why do electromagnetic, strong, and weak forces have spin-1 mediators, while gravity's hypothesized mediator has spin 2?

This question aims to explore the fundamental differences between gravity and other fundamental forces, focusing on why their force-carrying particles have different spins. I am not asking about the technical derivation of the graviton's spin from the Einstein-Hilbert action, but rather seeking to understand the physical or theoretical reasons behind this spin difference across forces.

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  • $\begingroup$ Well, the source of the gravitational field is the stress energy tensor (which is a spin two object) instead of a Lie algebra valued current (which is a spin one object). $\endgroup$
    – Gold
    Commented Aug 25 at 20:48
  • $\begingroup$ @Neutralino You need the opposite charges for dipole (spin-1) interactions. In gravity only one attractive charge exists, so only quadrupole (spin-2) interactions are possible. $\endgroup$
    – safesphere
    Commented Aug 27 at 5:00

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There's different levels of sophistication you could give to this question, but at the most basic level: empirically, general relativity is an extremely successful theory of gravity and agrees with observations every time we can test it. So, we tend to trust it's predictions as a reasonable, default hypothesis even when we cannot directly verify them.

General relativity predicts gravitational waves have a spin-2 character. While we've never directly measured the polarization (beyond ruling out some extreme, strawman possibilities), many other predictions of GR with respect to gravitational waves have turned out to be correct (such as the spin-down rate of the Hulse-Taylor pulsar, the direct detection of gravitational waves by LIGO/Virgo from compact binary systems, the speed of gravitational waves, etc). According to the normal rules of quantization, classical gravitational waves become gravitons. So we expect spin-2 polarized classical gravitational waves to correspond to a spin-2 graviton after quantization.

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  • $\begingroup$ This seems to be more explaining why we believe that the graviton has spin 2, rather than why it is spin-2. $\endgroup$
    – Acccumulation
    Commented Aug 26 at 4:56
  • $\begingroup$ IIRC "agrees with observations every time we can test it" is true but has one catch: we cannot test it precisely enough in a range wide enough. For example according to the Wiki the measurement of acceleration of free fall has at best the accuracy 10e-11 while Schwarzschield's modification rs/r has the order of magnitude 10e-13. $\endgroup$
    – user13964273
    Commented Aug 26 at 12:43
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From a theoretical point of view you can see this as the fact that the 3 standard model interactions are forces (they generate 1D displacements), while in general relativity gravity exerts deformations* (which are described roughly as 2D displacements).

1D displacements are described by vectors (i.e. spin-1 objects) while deformations are described by particular rank-2 tensors (i.e. spin-2 objects). This is the reason.

Why gravity does exerts those deformations instead of forces and is so different is yet to discover.

*Deformations are intended, roughly, as the application of force in 2 different directions, usually not collinear, so that it deforms the path and shape of objects immersed in the gravitational field

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  • $\begingroup$ “Why gravity does exerts those deformations instead of forces and is so different is yet to discover.” - No, it is a common knowledge why there are no dipole (spin-1) gravitational waves. In the simplest case of spherical symmetry the Birkhoff theorem explains this. $\endgroup$
    – safesphere
    Commented Aug 27 at 4:50
  • $\begingroup$ @safesphere yes i know that, it's just a different way of saying the same concept. What i meant as something to discover is why all of this apply only to gravity and not to other forces, or equivalently why general relativity differs so much with yang-mills theory $\endgroup$
    – LolloBoldo
    Commented Aug 27 at 10:34
  • $\begingroup$ Because gravity has only one type of charge - attractive. $\endgroup$
    – safesphere
    Commented Aug 27 at 15:01
  • $\begingroup$ @safesphere that is a synonimous of spin-2 (weinberg explains this very well), they are all different ways of saying the same thing, but why gravity it is the way it is, it's still under research :) $\endgroup$
    – LolloBoldo
    Commented Aug 27 at 17:32
  • $\begingroup$ Why gravity is only attractive is given experimentally and explained by General Relativity. There is no mystery here. So It is unclear what exactly you see as “unknown” or “not understood” about gravity or what specific research you refer to. “Spin-2” in itself is a quantum thing, but its reasons are purely classical and there is nothing unknown about gravity at the classical level. $\endgroup$
    – safesphere
    Commented Aug 27 at 22:18

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