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Comment by lightsighter
The clever thing about interferometers is that they're actually measuring space and time in two different dimensions concurrently and then looking for changes in the interference pattern between light moving along each of the dimensions. Simplistically, imagine a gravitational wave propagating along one dimension of the interferometer (realistically gravitational waves will never be perfectly aligned with any direction of the interferometer). Space will be distorted in that dimension but not the other and we can notice the change in the resulting interference pattern. In practice, gravitational waves will come from all sorts of weird angles, but they will distort each of the two dimensions differently and allow us to figure what direction they were propagating by the interference pattern that's observed.