Recovering general relativity from a Planck scale discrete theory of quantum gravity
File(s)
Published version
Author(s)
Butterfield, Jeremy
Dowker, Fay
Type
Journal Article
Abstract
An argument is presented that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise within the theory, even if they are not its basis.
We lay out this argument in two claims. Roughly speaking, the first claim is that causal sets can recover continuum Lorentzian manifolds; and the second claim is that no other proposal for a set of discrete data that conforms to our sense of “fundamental discreteness at the Planck scale” is known to be able to recover continuum Lorentzian manifolds. To support this second claim, we show, in particular, that an apparent alternative discrete data set to causal sets, viz., a certain sort of combinatorial Lorentzian simplicial complex, cannot recover General Relativistic spacetimes in the appropriately unique way; for it cannot discriminate between Minkowski spacetime and a spacetime with a certain sort of gravitational wave burst.
We lay out this argument in two claims. Roughly speaking, the first claim is that causal sets can recover continuum Lorentzian manifolds; and the second claim is that no other proposal for a set of discrete data that conforms to our sense of “fundamental discreteness at the Planck scale” is known to be able to recover continuum Lorentzian manifolds. To support this second claim, we show, in particular, that an apparent alternative discrete data set to causal sets, viz., a certain sort of combinatorial Lorentzian simplicial complex, cannot recover General Relativistic spacetimes in the appropriately unique way; for it cannot discriminate between Minkowski spacetime and a spacetime with a certain sort of gravitational wave burst.
Date Issued
2024
Date Acceptance
2024-03-21
Citation
Philosophy of Physics, 2024, 2 (1)
ISSN
2753-5908
Publisher
LSE Press
Journal / Book Title
Philosophy of Physics
Volume
2
Issue
1
Copyright Statement
© 2024 The Author(s). This
is an open-access article
distributed under the terms
of the Creative Commons
Attribution 4.0 International
License (CC-BY 4.0),
which permits unrestricted
use, distribution, and
reproduction in any
medium, provided the
original author and source
are credited. See http://
creativecommons.org/
licenses/by/4.0/
is an open-access article
distributed under the terms
of the Creative Commons
Attribution 4.0 International
License (CC-BY 4.0),
which permits unrestricted
use, distribution, and
reproduction in any
medium, provided the
original author and source
are credited. See http://
creativecommons.org/
licenses/by/4.0/
License URL
Identifier
http://dx.doi.org/10.31389/pop.17
Publication Status
Published
Article Number
5
Date Publish Online
2024-05-10