Layman said:
If I don't understand, or agree with, a statement about SRT made by another poster in this forum, am I supposed to refrain from expressing disagreement?
It depends on why you disagree, and how you express the disagreement.
For example, if someone were to say on these forums that "special relativity uses Galilean transformations to go from one inertial frame to another", you would be quite justified in pointing out that that's false; SR uses Lorentz transformations, not Galilean ones.
But if someone says that, in SR, the concept of an "absolute frame of reference" is not valid, and you disagreed with that, you would have to be careful how you expressed that disagreement, because your disagreement would be wrong: SR *does* say that the concept of an "absolute frame of reference" is not valid (more precisely, it's not valid within the context of SR as a theory; SR as a theory has no room for it, doesn't use it, and doesn't assign any meaning or weight to it). All inertial frames are equivalent in SR, in the sense that they are all equally valid for expressing physical laws. Disagreeing with that statement, or even appearing to disagree with it, just leads to pointless threads that go on forever; those of us who have been here on PF for a while have seen it happen all too many times, which is why we try pretty hard to nip it in the bud if it looks like it's happening again.
In your case, you implicitly equated measuring the CMBR with measuring an "absolute frame of reference". What you should have done, IMO, was to ask a question something like this: "I can measure the CMBR, and that measurement picks out a particular frame of reference: the one in which the CMBR is isotropic. How does relativity reconcile that with the principle that all inertial frames are equivalent?" That would have made it clearer that you were not trying to claim that SR was wrong; you were just trying to understand how SR reconciles two things that look, on the surface, like they don't fit together. (There are a *lot* of examples in relativity where things look, on the surface, like they don't fit together, but can be reconciled perfectly well; so when you see things in relativity that look, on the surface, like they don't fit together, it's always a good idea to assume, or at least behave as if you assume, that there *is* a reconciliation at a deeper level and ask what it is.)
PAllen went ahead and gave a partial response to that question, even though you didn't ask it. A further response would be to say that inertial frames are equivalent for expressing physical laws, but obviously that doesn't mean that all inertial frames look the same in every respect. The physical laws say things like: the frequency you will measure for a particular photon (such as one in the CMBR) depends on your 4-velocity and the photon's 4-momentum. You can assess that in any inertial frame; the calculation may be simpler to do in the frame in which the CMBR is isotropic, but the same physical law can be expressed in any frame, and is equally valid in all of them. The experimental fact that the CMBR exists shows that the universe is filled with photons that have particular properties; but that in no way privileges the frame in which those photons look isotropic, from the standpoint of physical laws.
In the other thread you refer to, while the test theory studies you mention may have established that assuming that there is absolute motion can be reconciled with experiment (I'm not familiar enough with the studies to know whether they actually did that), you appear to me to have been making a stronger claim: that *Special Relativity*, that specific theory (as opposed to some generalized test theory of which SR is one special case), allows one to assume absolute motion. That's not correct; SR, the specific theory, has no room for a concept of absolute motion, any more than for a concept of an absolute reference frame. You also appeared to continue to insist that SR requires everyone to assume that they are "not moving", i.e., to always adopt an inertial frame in which they are at rest, even after at least two posters in that thread pointed out to you that SR doesn't require that.
Once again, I understand that these are things that look, on the surface, like they are difficult to reconcile; but your response should be to ask what the reconciliation is, not to repeat claims that you have already been told are wrong.