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Some people refer to cosmic microwave background's (CMB) frame of reference as an absolute one. If I understand correctly, we can measure 'absolute' velocity in this frame by using the Doppler effect. However, I don't know how we can know what the 'basis' frequency of CMB is (in its own frame)? Can it be obtained by some quantum-cosmological consideration?

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The velocity of Earth relative to the CMB frame is measured by observing the anisotropy of the CMB temperature.

The above data is the is the anisotropy of temperature of the CMB as measured by NASA U2 airplanes in the 1970s.

The anisotropy is due to the redshift and blueshift of the Earth moving 300 kilometers per second or 1,080,000 kilometers per hour relative to the frame of the CMB, in the direction of the + at the center of the red region of the plot. This is mostly due to the peculiar motion of the Milky Way toward the Great Attractor.

Note: in the figure red means hotter and blueshifted, blue means cooler and redshifted. The contours are 1 millikelvin intervals.

The "basis frequency" (as the question calls it) of the CMB would be the frequency of the temperature with zero anisotropy. Really it is a black body frequency distribution of temperature 2.725K.

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In another sense, the "frame of the CMB" is the frame from which it was emitted c. 13bn years ago. In that frame it is (was?) rather hotter ;-) Maybe 4000K or so, red-shifted to 2.725K? –  Steve Jessop May 27 at 23:27
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