I remember an analogy that explained this phenomenon using magnetic field, a charged particle will experience a force next to another spinning charged particle or something like that. But I don't want to confused this with time dilation so what exactly do frame dragging do to a photon as seen by outside observer? Probe B experiment only seems to validate the existence of this phenomenon by looking for a precession from a gyroscope then what about a photon?
Indeed a central assertion of relatativistic physics is that any local setup will identify the same coordinate system as the local inertial coordinate system.
In terms of propagating electromagnetic waves the counterpart of a mechanical gyroscope is a ring laser gyroscope.
The operating principle of a ring laser gyro is the Sagnac effect.
There are small ring laser gyroscope designs that are used in aircrafts and ships to measure rotation rate.
Around the world there are a couple of stations where a large ring laser gyroscope is used to perform high resolution measurement of the Earth rotation rate.
These high performance instruments are sensitive enough to pick up ground motion due to earth quakes from all over the world.
The researchers also hope that over time the measurement accuracy can be increased to such a level that frame dragging can be corroborated.
At the geodesics observatory in Wettzell, Germany a square, 4 by 4 meter ring laser gyroscope is operated. (To my knowledge this facility is still in operation as of now, march 2021)
In 2015 the ROMY facility was built (ROMY, ROtational Motions in seismologY) The ROMY facility has 4 triangular ring laser gyroscopes, arranged as a tetrahedron. These triangles have a perimeter of 20 meters.