A regularized photon-pair geometry motivated by the ER=EPR conjecture
Abstract
We regularize the Aichelburg-Sexl shock-wave geometry for massless particles by smearing the point-like source over a string-inspired length scale l0. A radial extension of the transverse geometry admits a zero-throat Einstein-Rosen interpretation. For a photon wave packet of longitudinal extent L, the regularized gravitational self-energy of a transversely separated pair is EGSE∼ 4G(ℏω)2/c4L ln (d2/l02), where d is the transverse separation. The factor 1/L strongly suppresses the interaction, giving gravitational stability times greater than 1030 years for optical photons. We also examine an effective two-dimensional entanglement-entropy description of the shock-wave geometry. The entropy construction reproduces the same dependence on the scales d, L, and l0, and can be calibrated to reproduce the normalization of the direct self-energy calculation. However, we find that the gravitationally induced excess entropy, and hence the self-energy inferred from this prescription, is the same for Bell-entangled and unentangled photon pairs having identical energy-momentum distributions. This agrees with the direct geometrical calculation, since the classical two-shock metric depends on the stress-energy tensor but not on the polarization entanglement. The present construction should therefore be understood as a semiclassical ER-like geometry motivated by ER=EPR, rather than as a complete realization of the conjecture. A geometry whose connectivity tracks the amount of quantum entanglement would require a quantum-gravitational description sensitive to state-dependent correlations beyond the one-point stress-energy tensor.
Versions
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BibTeX
@misc{jusufi2026regularized,
title = {{A regularized photon-pair geometry motivated by the ER=EPR conjecture}},
author = {Kimet Jusufi and Francisco S. N. Lobo and Douglas Singleton},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.02943},
eprint = {2606.02943},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.02943},
}
RIS
TY - UNPB
TI - A regularized photon-pair geometry motivated by the ER=EPR conjecture
AU - Kimet Jusufi
AU - Francisco S. N. Lobo
AU - Douglas Singleton
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2606.02943
UR - https://arxiv.org/abs/2606.02943
AB - We regularize the Aichelburg-Sexl shock-wave geometry for massless particles by smearing the point-like source over a string-inspired length scale l_0. A radial extension of the transverse geometry admits a zero-throat Einstein-Rosen interpretation. For a photon wave packet of longitudinal extent L, the regularized gravitational self-energy of a transversely separated pair is E_GSE∼ 4G(ℏω)^2/c^4L ln (d^2/l_0^2), where d is the transverse separation. The factor 1/L strongly suppresses the interaction, giving gravitational stability times greater than 10^30 years for optical photons. We also examine an effective two-dimensional entanglement-entropy description of the shock-wave geometry. The entropy construction reproduces the same dependence on the scales d, L, and l_0, and can be calibrated to reproduce the normalization of the direct self-energy calculation. However, we find that the gravitationally induced excess entropy, and hence the self-energy inferred from this prescription, is the same for Bell-entangled and unentangled photon pairs having identical energy-momentum distributions. This agrees with the direct geometrical calculation, since the classical two-shock metric depends on the stress-energy tensor but not on the polarization entanglement. The present construction should therefore be understood as a semiclassical ER-like geometry motivated by ER=EPR, rather than as a complete realization of the conjecture. A geometry whose connectivity tracks the amount of quantum entanglement would require a quantum-gravitational description sensitive to state-dependent correlations beyond the one-point stress-energy tensor.
ER -