Wojtak, Hansen and Hjorth (Nature, 2011) have measured the long-predicted gravitational redshifts in galaxy clusters using Sloan Digital Sky Survey data. The effect is very small, corresponding to a velocity shift of only ~10 km/s in clusters with internal random motions ~600 km/s, but is in good agreement with general relativity predictions and possibly in conflict with some alternative gravity theories. Zhao, Peacock and Li (2012) showed that the measured shift includes a competing special relativistic effect - the transverse Doppler (TD) redshift - which is of similar magnitude.
In this talk I will describe how there are two more kinematic effects that need to be considered in interpreting these observations; a `light cone' effect that augments the TD shift and a competing effect caused by modulation of the surface brightness of galaxies by relativistic beaming.
I will discuss how these observations constrain gravitation theory, and along the way discuss some issues concerning the interpretation of astronomical redshifts in a broader context. I will also mention how the physics here echoes an interesting debate that took place in the 60's regarding the transformation of thermodynamic variables under Lorentz boosts.