Abstract
We study the bending of gravitons that pass near a massive object like the Sun, using scattering amplitudes in which the Sun is represented by a massive scalar particle. Our results complete previous work on the bending angles of massless spin-0, spin-$\frac{1}{2}$ and spin-1 particles, and provides more evidence for the violation of the equivalence principle at the quantum level, in the sense that the quantum corrections to bending angles for massless particles with different spins are different. We provide a universal expression for the bending angle in terms of coefficients of triangle and bubble integrals in the amplitudes in the low energy limit. We also compare bending angles for scalar, photon and graviton projectiles under different circumstances.
Highlights
General relativity and quantum mechanics have vastly different foundations
Our work provides more evidence for the violation of the classical principle of equivalence at the quantum level
In addition to the pure-graviton case, we provide a universal expression for the bending angle for scalar, photon and graviton projectiles in different setups, in terms of the amplitudes’ scalar integral coefficients in the low-energy limit
Summary
General relativity and quantum mechanics have vastly different foundations. The former requires a smooth spacetime and locality is absolute, while the latter requires regulation of short spacetime distances and locality is inherently smeared by the uncertainty principle. Later, using traditional Feynman rules, contributions from scalars (photons) crossing the cut were computed for the case of a scalar (photon) projectile [22] These papers found the expected classical post-Newtonian correction to the bending angle for any projectile, while the quantum corrections differ for particles with different spins. We find the expected classical post-Newtonian correction to the bending angle, but a different quantum correction from what was found in the scalar and photon cases. In addition to the pure-graviton case, we provide a universal expression for the bending angle for scalar, photon and graviton projectiles in different setups, in terms of the amplitudes’ scalar integral coefficients in the low-energy limit. We compare the various values of the bending angle and comment briefly on the possible origin of the violation of the classical equivalence principle found here and in Refs. [20,21,22]
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