### 2.2 Gravitational wave polarizations

Because of the equivalence principle, single isolated particles cannot be used to measure gravitational
waves: they fall freely in any gravitational field and experience no effects from the passage of the wave.
Instead, one must look for inhomogeneities in the gravitational field, which are the tidal forces carried by
the waves, and which can be measured only by comparing the positions or interactions of two or more
particles.
In general relativity, gravitational radiation is represented by a second rank, symmetric trace-free tensor.
In a general coordinate system, and in an arbitrary gauge (coordinate choice), this tensor has ten
independent components. However, as in the electromagnetic case, gravitational radiation has only
two independent states of polarization in Einstein’s theory: the plus polarization and the cross
polarization (the names being derived from the shape of the equivalent force fields that they
produce). In contrast to electromagnetic waves, the angle between the two polarization states
is rather than . This is illustrated in Figure 1, where the response of a ring of
free particles in the plane to plus-polarized and cross-polarized gravitational waves
traveling in the -direction is shown. The effect of the waves is to cause a tidal deformation of
the circular ring into an elliptical ring with the same area. This tidal deformation caused by
passing gravitational waves is the basic principle behind the construction of gravitational wave
antennas.

The two independent polarizations of gravitational waves are denoted and . These are the two
primary time-dependent observables of a gravitational wave. The polarization of gravitational waves from a
source, such as a binary system, depends on the orientation of the dynamics inside the source relative to the
observer. Therefore, measuring the polarization provides information about, for example, the orientation of
the binary system.