While Einstein’s general relativity predicts only two independent polarizations, there are other
theories of gravitation in which there are additional states of polarization. For instance, in
Fierze–Jordan–Brans–Dicke theory [394] there are four polarization degrees of freedom more than in
Einstein’s theory. Therefore, an unambiguous determination of the polarization of the waves will be of
fundamental importance.
In the case of a burst source, to determine two polarization states, source direction and amplitude
requires three detectors, observing other polarizations would require the use of more than three detectors
(see, for example, Will [394]). The scalar polarization mode of Brans–Dicke, for example, expands a
transverse ring of test particles without changing its shape. This is the breathing mode, or monopole
polarization. If such a wave is incident from above on an interferometer, it will not register
at all. But if it comes in along one of the arms, then, since it acts transversely, it will affect
only the other arm and leave a signal. If the wave is seen with enough detectors, then it is
possible to determine that it has scalar polarization. Note that a measurement such as this
can make a qualitative change in physics: a single measurement could put general relativity in
jeopardy.
Polarization measurements have an important application in astronomy. The polarization of the waves contains orientation information. For example, a binary system emits purely circular polarization along the angular momentum axis, but purely linear polarization in its equatorial plane. By measuring the polarization of waves from a binary (or from a spinning neutron star) one can determine the orientation and inclination of its spin axis. This is a piece of information that is usually very hard to extract from optical observations. We will return to this discussion in Section 7.1.1.
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