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Relative to what? That makes no sense.
Relative to the Cosmic Microwave Background. Seems to be the closest thing to an absolute reference frame.
The cosmic microwave background has no center, any claims that it even has a direction is controversial.
Is it controversial? I thought it was pretty established. In Wikipedia it says:
From the CMB data, it is seen that the Sun appears to be moving at 369.82±0.11 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB). The Local Group — the galaxy group that includes our own Milky Way galaxy — appears to be moving at 620±15 km/s in the direction of galactic longitude ℓ = 271.9°±2°, b = 30°±3°.[88] The dipole is now used to calibrate mapping studies.
Don't cite Wikipedia. Look at the tiny numbers in blue, click the one next to the statement you want to verify, it will show you the source of the information at the bottom of the page next to the matching number.
Well, following the main reference in the Wikipedia page leads to this:
The implied velocity for the Solar System barycenter is v = 369.82 ± 0.11 km s−1, assuming a value T0 = Tγ , towards (l, b) = (264.021◦ ± 0.011◦, 48.253◦ ± 0.005◦) [13]. Such a Solar System motion implies a velocity for the Galaxy and the Local Group of galaxies relative to the CMB. The derived value is vLG = 620 ± 15 km s−1 towards (l, b) = (271.9◦ ± 2.0◦, 29.6◦ ± 1.4◦) [13], where most of the error comes from uncertainty in the velocity of the Solar System relative to the Local Group. The dipole is a frame-dependent quantity, and one can thus determine the ‘CMB frame’ (in some sense this is a special frame) as that in which the CMB dipole would be zero. Any velocity of the receiver relative to the Earth and the Earth around the Sun is removed for the purposes of CMB anisotropy studies, while our velocity relative to the Local Group of galaxies and the Local Group’s motion relative to the CMB frame are normally removed for cosmological studies. The dipole is now routinely used as a primary calibrator for mapping experiments, either via the time- varying orbital motion of the Earth, or through the cosmological dipole measured by satellite experiments.
Do any references suggest this dipole is under debate?
Ok, I guess the idea that the CMB suggests movement relative to a quasi-absolute reference frame really has become disputed lately... I also found this newer paper by the same authors. It's a pity, I liked the idea.
Same, it gave credence to the concept of a potential center of the big bang being something we could find and observe, which is just really cool to think about.