We pose and resolve a holographic puzzle regarding an apparent violation of
causality in AdS/CFT. If a point in the bulk of $AdS$ moves at the speed of
light, the boundary subregion that encodes it may need to move superluminally
to keep up. With $AdS_3$ as our main example, we prove that the finite extent
of the encoding regions prevents a paradox. We show that the length of the
minimal-size encoding interval gives rise to a tortoise coordinate on
$AdS$ that measures the nonlocality of the encoding. We use this
coordinate to explore circular and radial motion in the bulk before passing to
the analysis of bulk null geodesics. For these null geodesics, there is always
a critical encoding where the possible violation of causality is barely
avoided. We show that in any other encoding, the possible violation is
subcritical.
Description
The Tortoise and the Hare: A Causality Puzzle in AdS/CFT
%0 Generic
%1 berenstein2020tortoise
%A Berenstein, David
%A Grabovsky, David
%D 2020
%K arxiv
%T The Tortoise and the Hare: A Causality Puzzle in AdS/CFT
%U http://arxiv.org/abs/2011.08934
%X We pose and resolve a holographic puzzle regarding an apparent violation of
causality in AdS/CFT. If a point in the bulk of $AdS$ moves at the speed of
light, the boundary subregion that encodes it may need to move superluminally
to keep up. With $AdS_3$ as our main example, we prove that the finite extent
of the encoding regions prevents a paradox. We show that the length of the
minimal-size encoding interval gives rise to a tortoise coordinate on
$AdS$ that measures the nonlocality of the encoding. We use this
coordinate to explore circular and radial motion in the bulk before passing to
the analysis of bulk null geodesics. For these null geodesics, there is always
a critical encoding where the possible violation of causality is barely
avoided. We show that in any other encoding, the possible violation is
subcritical.
@misc{berenstein2020tortoise,
abstract = {We pose and resolve a holographic puzzle regarding an apparent violation of
causality in AdS/CFT. If a point in the bulk of $AdS$ moves at the speed of
light, the boundary subregion that encodes it may need to move superluminally
to keep up. With $AdS_3$ as our main example, we prove that the finite extent
of the encoding regions prevents a paradox. We show that the length of the
minimal-size encoding interval gives rise to a tortoise coordinate on
$\mathrm{AdS}$ that measures the nonlocality of the encoding. We use this
coordinate to explore circular and radial motion in the bulk before passing to
the analysis of bulk null geodesics. For these null geodesics, there is always
a critical encoding where the possible violation of causality is barely
avoided. We show that in any other encoding, the possible violation is
subcritical.},
added-at = {2020-11-21T00:12:14.000+0100},
author = {Berenstein, David and Grabovsky, David},
biburl = {https://www.bibsonomy.org/bibtex/26fe36209de7ec60e7dbf3515d399cdaa/nimaaj},
description = {The Tortoise and the Hare: A Causality Puzzle in AdS/CFT},
interhash = {06df90a80190946f2a046e03e51e321f},
intrahash = {6fe36209de7ec60e7dbf3515d399cdaa},
keywords = {arxiv},
note = {cite arxiv:2011.08934Comment: 28 pages, 14 figures},
timestamp = {2020-11-21T00:12:14.000+0100},
title = {The Tortoise and the Hare: A Causality Puzzle in AdS/CFT},
url = {http://arxiv.org/abs/2011.08934},
year = 2020
}