# What is the meaning of “current” CMB rest frame or the CMB rest frame at redshift $z$?

As I know that the definition of the CMB rest frame is the comoving frame of the plasma emitting CMB. And the anisotropy of CMB is due to the velocity difference between the earth frame and the CMB frame. But I have read a textbook mentioning that observers are at rest with the current CMB proper frame and a star at $$z$$ should be at rest with the CMB proper frame at $$z$$. What is the meaning of "current" CMB proper frame?

• Either I've never heard of this or I'm missing context. Can you cite the source so we can check it out? – Jim Nov 5 '20 at 13:43
• Are you familiar with the difference between proper distance & comoving distance? en.wikipedia.org/wiki/Comoving_and_proper_distances Also see physics.stackexchange.com/q/257842/123208 & physics.stackexchange.com/q/153926/123208 – PM 2Ring Nov 5 '20 at 14:04
• The reason I asked to see the source is because this sounds like the most obfuscated way to explain that recessional velocity isn't proper velocity. But it would be silly for any textbook to explain it this way, so I figure I must be missing context or this is a concept that I haven't heard of. My default is to assume nothing until I can see the source and check if there are any misunderstandings here – Jim Nov 5 '20 at 14:24
• @Jim The source is from "the physics of gamma-ray burst" by Bing Zhang. – ewittmyl Nov 5 '20 at 15:43
• any particular page number? – Jim Nov 5 '20 at 16:29