Bending of Light in Quantum Gravity

Abstract

We consider the scattering of lightlike matter in the presence of a heavy scalar object (such as the Sun or a Schwarzschild black hole). By treating general relativity as an effective field theory we directly compute the nonanalytic components of the one-loop gravitational amplitude for the scattering of massless scalars or photons from an external massive scalar field. These results allow a semiclassical computation of the bending angle for light rays grazing the Sun, including long-range contributions. We discuss implications of this computation, in particular the violation of some classical formulations of the equivalence principle.PACS numbers: 04.62.+v, 04.80.Cc Since the discovery of quantum mechanics and general relativity in the previous century it has been clear that these two theories have completely different notions of reality at a fundamental level. While deterministic physics is a crucial ingredient in general relativity, i.e., particles follow field equations formulated as geodesic equations, in quantum mechanics such a concept has no meaning since one has to accept that space and momentum are mutually complementary concepts. The notion of a quantum field theory offers a middle ground to some extent by combining these concepts through field variables, but the traditional formulation of such a theory suffers from (nonrenormalizable) divergences in the ultraviolet regime. Whatever the high-energy theory of gravity turns out to be, it is intriguing that we can already answer a number of important questions simply by employing an effective field theory framework for general relativity, wherein the basic building block is the Einstein-Hilbert Lagrangian. In order to absorb ultraviolet divergences we include in the action all possible invariants allowed by the basic symmetries of the theory. This infinite set of corrections is usually seen as a signal of the loss of predictability and as a dependence on the high-energy completion of the theory. However, at one-loop order something surprising happens that was first noticed by [1] and was exploited in [2, 3]-the basic Einstein-Hilbert term is sufficient to extract the longrange behavior of the theory. This feature was used to extract the quantum corrections to the Newtonian potential of a small mass attracted by a larger mass:Here M is a large (scalar) object, say the Sun, m is a small test mass, r is the distance between the two objects, and G, c and , are Newton's constant, the speed of light and the Planck constant respectively. Since these initial computations there have appeared a number of papers computing various potentials [4], involving e.g., fermionic and spin-1 matter. It has been explicitly demonstrated that the spin-independent components of one-loop general relativity theory display universality both for the classical contribution as well as for the one-loop quantum correction [3,4].In this Letter we will focus on a different problem, which has not yet been discussed in the literature, namely computing the leading quantum correction to t...

Light-like scattering in quantum gravity

“…We see that the eikonal approximation leads to the expected classical general relativity contributions, in agreement with the next-to-leading correction of [55] and [57], as well as producing the leading quantum correction. Treating the quantum effect using the eikonal procedure, we recover the results of [22] derived with a semiclassical potential method. The quantum effect has the power-law dependence in impact parameter as the classical post-post-Newtonian contribution.…”

“…There is an equivalence between the eikonal method described above and the semiclassical potential method which we used in [22]. In order to elucidate this, it is useful to consider the bending in terms of a wave picture of light propagation.…”

“…Following [22], the generalization to the full interaction is then achieved by replacing the lowest order potential V 0 (r) by the full interaction potential V int (r) generated from the low energy approximation with t −q 2 of the total gravitational scattering amplitude 4 in eq. (4.9) with the second Born (rescattering) term excised…”

“…Though such a theory has yet to be found, today we can address profound practical and reliable (low energy) consequences of the (currently unknown) underlying quantum theory through the modern viewpoint of effective field theory (EFT) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The EFT framework allows direct exploration of various quantitative phenomenological applications, see for example [24,25].…”

Five-loop four-point integrand of N=8 supergravity as a generalized double copy

“…The duality has been crucial in the construction of numerous gravity multiloop amplitudes [4,11,31,32], where it has been used to identify new nontrivial ultraviolet cancellations in N = 4 and N = 5 supergravity [13,15], known as 'enhanced cancellations'. Apart from offering a simple means for obtaining loop-level scattering amplitudes in a multitude of (super)gravity theories, the duality also addresses the construction of black-hole and other classical solutions [33] including those potentially relevant to gravitational-wave observations [34], corrections to gravitational potentials [35], the relation between supergravity symmetries and gauge-theory ones [20,22,36], and the construction of multiloop form factors [37]. The duality has also been identified in a wider class of quantum field and string theories [30,[38][39][40][41].…”