The Transverse-Traceless Spin-2 Gravitational Wave Cannot Be A Standalone Observable Because It Is Acausal. (arXiv:1902.03294v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Chu_Y/0/1/0/all/0/1">Yi-Zen Chu</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Liu_Y/0/1/0/all/0/1">Yen-Wei Liu</a>
We show, through an explicit calculation of the relevant Green’s functions,
that the transverse-traceless (TT) portion of the gravitational perturbations
of Minkowski spacetime and of spatially flat cosmologies with a constant
equation-of-state $w$ receive contributions from their isolated matter
source(s) outside the past null cone of the observer. This implies the TT
gravitational wave (GW) cannot be a standalone observable — despite widespread
(apparent) claims in the gravitational wave literature to the contrary. About a
Minkowski background, all 4 of the gauge-invariant variables — the two
scalars, one vector and tensor — play crucial roles to ensure the spatial
tidal forces encoded within the gauge-invariant linearized Riemann tensor are
causal. These gravitational tidal forces do not depend solely on the TT
graviton but rather on the causal portion of its acceleration. However, in the
far zone radiative limit, the flat spacetime `TT’ graviton Green’s function
does reduce to the causal `tt’ ones, which are the ones commonly used to
compute gravitational waveforms. Similar remarks apply to the spin-1 photon;
for instance, the electric field does not depend solely on the photon, but is
the causal part of its velocity. As is known within the quantum theory of
photons and linearized gravitons, there are obstacles to the construction of
simultaneously gauge-invariant and Lorentz-covariant descriptions of these
massless spin-1 and spin-2 states. Our results transparently demonstrate that
the quantum operators associated with the helicity-1 photon and helicity-2
linear graviton both violate micro-causality: namely, they do not commute
outside the light cone in flat and cosmological spacetimes.
We show, through an explicit calculation of the relevant Green’s functions,
that the transverse-traceless (TT) portion of the gravitational perturbations
of Minkowski spacetime and of spatially flat cosmologies with a constant
equation-of-state $w$ receive contributions from their isolated matter
source(s) outside the past null cone of the observer. This implies the TT
gravitational wave (GW) cannot be a standalone observable — despite widespread
(apparent) claims in the gravitational wave literature to the contrary. About a
Minkowski background, all 4 of the gauge-invariant variables — the two
scalars, one vector and tensor — play crucial roles to ensure the spatial
tidal forces encoded within the gauge-invariant linearized Riemann tensor are
causal. These gravitational tidal forces do not depend solely on the TT
graviton but rather on the causal portion of its acceleration. However, in the
far zone radiative limit, the flat spacetime `TT’ graviton Green’s function
does reduce to the causal `tt’ ones, which are the ones commonly used to
compute gravitational waveforms. Similar remarks apply to the spin-1 photon;
for instance, the electric field does not depend solely on the photon, but is
the causal part of its velocity. As is known within the quantum theory of
photons and linearized gravitons, there are obstacles to the construction of
simultaneously gauge-invariant and Lorentz-covariant descriptions of these
massless spin-1 and spin-2 states. Our results transparently demonstrate that
the quantum operators associated with the helicity-1 photon and helicity-2
linear graviton both violate micro-causality: namely, they do not commute
outside the light cone in flat and cosmological spacetimes.
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