
Gravitational waves may oscillate, just like neutrinos - alansammarone
https://phys.org/news/2017-09-gravitational-oscillate-neutrinos.html
======
raattgift
Firstly, thank you phys.org for including a link to the arXiv preprint. :-)

Secondly, this comment grew a lot while I was composing it, and it turns into
two comments: a crash-speed overview of some aspects of linearized gravity and
a few paragraphs describing what's in this paper, forming a quick personal
reaction from a pseudonymous nobody.

Thirdly, massive gravity theory is not really new, and the 2010 date in the
phys.org writeup refers to a solution for massive gravity in 4-dimensional
spacetime by de Rham, Gabadadze and Tolley (
[https://arxiv.org/abs/1011.1232](https://arxiv.org/abs/1011.1232) ).
Previously, stable solutions were only known in lower dimensioned spacetimes.
However, there have been fits and starts of work on this broad family of
gravity theories dating to Pauli & Fierz, who proposed a massive spin-two
field on a flat spacetime in the 1960s (Blasi & Maggiore give some details at
[https://arxiv.org/abs/1706.08140](https://arxiv.org/abs/1706.08140) ).

In order to talk about this (dense, technical!) paper, I think one needs to
know a little about about perturbatively quantized gravity, which I'll
describe over a few paragraphs. You can skip ahead a bit by just accepting
that gravitons exchanged by _everything_ (including each other) and that in
standard General Relativity gravitons are massless.

When you take a perturbation theory approach to the metric of General
Relativity, you fix a background spacetime (which is almost always flat, i.e.
described with the Minkowski metric), which gets the label \eta (the
solvable), with deviations from \eta held in h (the perturbation). The metric
becomes g = \eta + h. Some configurations of moving mass-energy can produce
waves in h that propagate according to the (classical) massless wave equation
on flat spacetime, analogously to (classical) electromagnetic waves on flat
spacetime.

One can proceed to quantize h. Well, really first one expands g = \eta + h +
h^2 + h^3 + ... where h^2 etc are quadratic, cubic, and higher-order terms in
the perturbation. Next one omits as many of the higher-order terms as one can
get away with. In linearized gravity, that means h^2 and up are ignored.

Essentially we turn classical waves in h into large numbers of particles we
call gravitons, much as one turns classical electromagnetic waves into large
numbers of photons. I omitted indices and a couple of other details (most
notably gauge fixing) nevertheless g, \eta and h are all symmetric rank-two
tensors. The result of the quantization of (symmetric rank-2 tensor) h is
therefore a massless spin-2 gauge boson, which compares with the quantization
of electromagnetic waves (as antisymmetric rank-2 tensors [4]) resulting in a
massless spin-1 gauge boson.

This is perturbative quantum gravity, a real working quantum theory of
gravity, but not a candidate for a more fundamental theory than General
Relativity because higher order terms in h are important in a universe with
compact massive objects, and we don't know how to include such higher-order
terms into this type of quantization.

There is a key pattern between the spin-1 and spin-2 particles: each mediates
an interaction between particles that carry a + or - charge.

    
    
        spin  like-charges opposite-charges
        ----  ------------ ----------------
        1     repel        attract
        2     attract      repel
    

The electromagnetic interaction is an example of one mediated a spin-1
particle, and matter may have an electromagnetic charge + or -. With a
suitable choice of gauge, matter may also have a gravitational charge, + or -.

In our universe, the electromagnetic interaction is much stronger than the
gravitational interaction, but not everything has an electromagnetic charge.
Most importantly, photons themselves do not have an electromagnetic charge. In
perturbatively quantized gravity though, _everything_ has a gravitational
charge, including gravitons.

If we take perturbatively quantized gravity seriously, in our patch of the
universe there is effectively nothing with the opposite gravitational charge
of stuff here on earth, probably for reasons similar to why there is
approximately no antimatter around us: segregation in the early universe.
Essentially why we see no anti-gravity is that even our positrons and
antiquarks have the same gravitational charge as everything else around us, so
they interact with only one of the possible graviton charges.

That gravitons of the same charge attract one another leads to the higher
order terms in h: their self-interaction is the source of non-linearity.

Finally, perturbatively quantized gravity allows us to define an energy scale
for the gravitational interaction: it is "low energy" when the quadratic and
higher-order terms in h simply do not matter; it is "high energy" or "strong
gravity" when they do. The non-linearities higher-order terms in expanded h
can be represented by one or more loops of gravitons in Feynman diagrams.

From this we have learned that "strong gravity" appears when the dilating
effects of curvature are apparent even at Planck lengths or Planck time, or
equivalently "high energy" appears around a tiny object with at least Planck
energy. In practice this only appears very close to whatever quantum state
there is in the place of classical gravitational singularities. Crucially this
is well inside the event horizons of black holes, or in the very early
universe. Consequently, perturbatively quantized gravity, and General
Relativity, are both reliable "low energy" effective field theories
practically everywhere we presently have the technology to study.

Next, on to bigravity.

~~~
raattgift
Now, on to bigravity.

It can be fun and interesting to investigate theories of gravity other than
General Relativity, and one popular strategy is to introduce extra degrees of
freedom. This paper deals with a family of such theories called bimetric
gravity (or "bigravity" as in the paper) where the extra degree of freedom is
a (classical) second rank-two tensor field.

Typically one runs into a bimetric theory where the second metric is energy-
dependent, and is simply not noticeable in weak gravity. Where one finds
strong gravity -- notably, in the very early universe -- the second metric
becomes important. A popular approach is that the second metric "steers" the
first metric. In our classical expansion g = \eta + h, the perturbations that
obey the equations for massive wave propagation instead obey the massless wave
equations. This drag on the waves means that (classical) electromagnetic waves
outrace (classical) gravitational waves when the second metric is operative.
This is often used in models to solve the horizon problem: why are readings of
the cosmic microwave background at opposite sides of our view of the universe
at the same temperature? Because light was fast enough to carry energy between
distantly separated matter, thermalizing it before gravitational collapse
could begin in earnest. [1][2]

When we quantize a bimetric theory, we get two gravitons: one that is the
standard massless spin-2, and the other which is a massive spin-2. The massive
graviton only interacts with the massless graviton, and in weak gravity there
simply aren't many of either type of graviton, so you don't see the
interaction. In strong gravity the densities of both types of graviton
inevitably lead to interactions. As in standard perturbatively quantized
gravity, the massless graviton mediates the gravitational interaction of
everything in the universe (including both types of graviton).

We can now look at this particular bigravity paper's non-novelty in its
Abstract: "... a second ... tensor ... [couples with the standard metric
tensor] ... such that one massless and one massive linear combination arise.
Only one ... tensor ... [couples] to matter" and have an idea what that means.
The novelty here is that the second -- massive -- tensor is not energy-
dependent, it's always there but gets "washed out" by the behaviour of the
tensor fields.

This novel behaviour, "oscillations", make sense in perturbatively quantized
gravity: we get two different gravitons, g_standard and g_massive, where
g_massive only interacts with g_standard, and g_standard interacts with
everything; when g_standard and g_massive are in the same point in the
background spacetime, there is a _linear_ effect [3] . g_standard continues to
propagate at the maximum speed (c), while wave packets of g_massive have a
lower group velocity. This is a tight analogy with neutrino oscillations where
heavier neutrinos move more slowly than the lightest neutrino, and where a
heavy sterile (no weak charge) neutrino exists.

This is a pretty wild claim. The authors believe their theory is self-
consistent, and propose some observables that are in detectable through
gravitational wave astronomy that we are close to being able to do. Roughly, a
spinning barbell arrangement of matter (two black holes in orbit can be seen
as the weights on the end of a vanishingly thin bar) sheds gravitational waves
-- and under the Max-Platscher-Smirnov model there is a drag on their
propagation compared under standard General Relativity. As a practical
example, this leads to a dependence on several parameters, including travel
time for the massive component, of gravitational waves detectable by LIGO: the
final "bloop" [3] will sound different for similar-mass mergers at different
redshifts.

There are a lot of other likely observables including ones that should appear
in the cosmic microwave background. Bimetric theories are notorious for
generating modes that seem unreasonable (and thus are unlikely to be there
when you look for them). However, the idea is a neat and provocative one that
is put across well, and so was worth publishing on that basis.

\- --

[1]
[https://www.wikiwand.com/en/Horizon_problem#/Variable_speed_...](https://www.wikiwand.com/en/Horizon_problem#/Variable_speed_of_light_theories)

[2]
[https://www.wikiwand.com/en/Variable_speed_of_light](https://www.wikiwand.com/en/Variable_speed_of_light)

[3]
[https://www.youtube.com/watch?v=TWqhUANNFXw](https://www.youtube.com/watch?v=TWqhUANNFXw)

[4]
[https://www.wikiwand.com/en/Electromagnetic_tensor](https://www.wikiwand.com/en/Electromagnetic_tensor)
("... an antisymmetric rank-2 tensor field—on Minkowski space.")

[5]
[https://www.wikiwand.com/en/Electrovacuum_solution](https://www.wikiwand.com/en/Electrovacuum_solution)
("... in which the only nongravitational mass-energy present is the field
energy of an electromagnetic field")

~~~
alansammarone
Thanks for this very detailed and well written comment. I'm a physics student,
so this is tremendously interesting and useful. Thanks.

