Fundamental question on GR: Basis vector meaning

[TrickyDicky]

I don't see what you think fails when you measure the Earth's velocity relative to the CMB. It's still a relative measurement. The frame is specified not by the existence of the CMB, but by its isotropy.

But I suspect we're far apart enough in our thinking that there's not a lot of sense talking about it. But I do feel some small obligation to point out there isn't any incosistency between measuring one's speed relative to the CMB and thinking that velocities are relative.

I would say precisely when there is differences in thinking (wich BTW I don't think are so far apart) is when forum debates are worth IMHO.

Nothing fails when measuring Earth's velocity wrt CMB, and there is no inconsistency in thinking that objects velocities are relative IMO.
What I pointed out is that you are considering the CMB an object and maybe you didn't realize it. Do you consider the CMB frame a material object?

 

[Ben Niehoff]

The CMB is a bunch of photons, so of course it's a material object.

2.7 K photons are arriving at our location from all directions. When we look at their power spectrum, we find a predominant dipole anisotropy that could be transformed away by a change in velocity. Therefore we conclude that the CMB measurements define a preferred frame: the one in which the dipole anisotropy vanishes. Hence we see that we have some nonzero velocity relative to this frame.

 

[TrickyDicky]

The CMB is a bunch of photons, so of course it's a material object.

a substance that pervade all the universe's space vacuum would you say?

2.7 K photons are arriving at our location from all directions. When we look at their power spectrum, we find a predominant dipole anisotropy that could be transformed away by a change in velocity. Therefore we conclude that the CMB measurements define a preferred frame: the one in which the dipole anisotropy vanishes. Hence we see that we have some nonzero velocity relative to this frame.

I see, preferred frame you say? How is it preferred?, looks like we haven't much choice with this one frame. It seems to me we are taking something that can't have motion like the CMB frame or vacuum as an absolute motion reference for the Earth's velocity, that appears more like an absolute frame than a preferred frame. Maybe you don't make distinctions between preferred and absolute frame of reference?

 

[WannabeNewton]

It is a preferred frame in that it is the frame in which the isotropy and homogeneity of the observed universe is made apparent. Note that we can choose frames in which space - like hypersurfaces do NOT have the properties of isotropy and homogeneity, and these frames would of course not be the CMB frame but we choose the CMB frame because it directly agrees with what we experimentally observe for our universe.

 

[TrickyDicky]

we choose the CMB frame because it directly agrees with what we experimentally observe for our universe.

Right, obviously we can chose whatever frame we want, I'm pointing out precisely that we choose this specific one for empirical reasons, and in this sense it looks like a natural choice rather than a "preferred" choice, even if any frame can be called preferred, if you choose it.
Can you see the difference?

 

[Ben Niehoff]

a substance that pervade all the universe's space vacuum would you say?

You say that like it's a bad thing...

I see, preferred frame you say? How is it preferred?, looks like we haven't much choice with this one frame. It seems to me we are taking something that can't have motion like the CMB frame or vacuum as an absolute motion reference for the Earth's velocity, that appears more like an absolute frame than a preferred frame. Maybe you don't make distinctions between preferred and absolute frame of reference?

The way the word "preferred" is intended in this context is simply that there is a physical situation that picks out a particular frame as being special. I don't mean "preferred" in the sense that I like this frame better than others, for example.

The laws of physics are Lorentz-invariant. But this does not mean that any specific physical configuration must be Lorentz-invariant. For example, if I put a massive body out in empty space, I've broken Lorentz invariance! Because now there is a preferred frame where the massive body is at rest. The physical situation has only SO(3) rotational symmetry, not full SO(3,1) Lorentz symmetry. If I put two massive bodies in space with zero angular momentum, the symmetry is further broken to SO(2). And if I give them orbital angular momentum, then there is no continuous symmetry left at all.*

* Correction: If they are in a circular orbit, then there is a continuous (affine) U(1) symmetry that is a combination of time translation and rotation in the plane of the orbit. This symmetry takes the double helix of their worldlines onto itself.

 

[TrickyDicky]

You say that like it's a bad thing...

Haha, not at all

The way the word "preferred" is intended in this context is simply that there is a physical situation that picks out a particular frame as being special. I don't mean "preferred" in the sense that I like this frame better than others, for example.

The laws of physics are Lorentz-invariant. But this does not mean that any specific physical configuration must be Lorentz-invariant. For example, if I put a massive body out in empty space, I've broken Lorentz invariance! Because now there is a preferred frame where the massive body is at rest. The physical situation has only SO(3) rotational symmetry, not full SO(3,1) Lorentz symmetry. If I put two massive bodies in space with zero angular momentum, the symmetry is further broken to SO(2). And if I give them orbital angular momentum, then there is no continuous symmetry left at all.*

* Correction: If they are in a circular orbit, then there is a continuous (affine) U(1) symmetry that is a combination of time translation and rotation in the plane of the orbit. This symmetry takes the double helix of their worldlines onto itself.

This is all fine, but these are artificial situations, all begin with "if I put such and such...".
What I'm saying is that the frame we encounter in the CMB is a "natural" frame, we don't have to put anythig, we just measure it.