Does electromagnetism plus gravity require new particles far below the Planck scale?
In plain words
Applying positivity rules to electrons and photons with gravity seems to demand new particles at an energy far below the Planck scale (the energy where quantum gravity becomes strong). It is unsettled whether this is a real prediction or an artifact of how the graviton contribution is handled.
Precise statement
For QED with electron mass $m_{e}$ and charge $e$ coupled to gravity, the one-loop light-by-light and gravitational contributions to the forward photon-photon amplitude violate the naive positivity bound unless new states appear at $\Lambda_{\mathrm{new}}\sim(e\,m_{e}\,M_{\mathrm{pl}})^{1/2}$, approximately $2 \times 10^{7}\ \text{to}\ 4 \times 10^{7}\ \mathrm{GeV}$ (reduced or unreduced Planck mass) (Alberte, de Rham, Jaitly, Tolley, Phys. Rev. D 103, 125020, 2021, obtained assuming the t-channel graviton pole can be discarded). Decide whether every consistent UV completion of QED plus gravity has new states below this scale, or whether the allowed Planck-suppressed negativity removes the requirement.
What would settle it
A rigorous gravitational positivity bound with controlled negativity, evaluated on the one-loop QED plus gravity amplitude.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Alberte, de Rham, Jaitly, Tolley (arXiv Dec 2020, PRD 2021) derived the low scale only under the assumption that the t-channel pole may be discarded, and conjectured that allowed negativity removes it; unresolved as of 2026.
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