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 Incoming links: Soft graviton theorem

Alexander Zhiboedov is a theoretical physicist who, with Andrew Strominger, connected gravitational memory to the Soft graviton theorem. Their 2014 preprint considers arrays of detectors before and after passage of a gravitational radiation pulse near future null infinity.

The resulting relative displacement reproduces gravitational memory, while its formula is related to the low-energy limit described by the Soft graviton theorem. This unites a lasting change in detector separation with an apparently different statement about emission of very low-energy gravitons.^[ref]

A pulse need not leave only a passing oscillation: it can produce a lasting relative displacement between freely moving detectors. Their calculation links that displacement to the radiation energy flux, making a measurable classical effect part of a broader relationship with low-energy quantum emission.^[ref]

q

M^{μ} (q) = (\sum_{i} η_{i} Q_{i} \frac{p _{i}^{μ}}{p _{i} \cdot q}) M_{0} + O (q^{0}),

where

η_{i} = + 1

for outgoing and

- 1

for incoming particles. Contracting with

q_{μ}

and applying the Ward identity gives

(\sum_{i} η_{i} Q_{i}) M_{0} = 0.

For a nonzero underlying amplitude, total outgoing charge equals total incoming charge. Thus photon gauge redundancy enforces conservation of electric charge.

The analogous Soft graviton theorem for helicity two requires universal coupling to energy-momentum and yields conservation of total four-momentum, the seed of the equivalence principle. For massless helicity greater than two, the corresponding soft consistency conditions demand conserved higher-rank momentum charges that generic interacting scattering cannot satisfy. Under the assumptions of a Lorentz-invariant local S-matrix with long-range interactions, such particles therefore have no nontrivial coupling; this is the soft-theorem obstruction to interacting massless higher-spin particles.