Relative motion of an arbitrary volume of space ( is space static or dynamic?) Do physicists consider space as being "static" or "dynamic" ?  
Hi I asked a question about whether space can move, and from the answer, I realized I was not precise enough and did not actually ask what I thought I was asking.
Sorry. This is therefore not the same question which was asked before (and well answered), but very similar, so I hope it gets answered. Thanks
I am not referring to the entire whole spacetime of the universe, but to what I would call an arbitrary bubble of space
Perhaps it is helpful to give a definition here.
What I would call an arbitrary bubble of space is a relatively small spherical volume of space that has  a center, which at a given time can be assigned a given distance from an observer.  


*

*So my question is can such an arbitrary bubble of space have a motion relative to an observer on earth?


I think it can by the following common sense arguments, but I am always surprised that sometimes there are very good reasons why common sense is not applicable.
My reasoning:
We have chosen the meter as the length of the path traveled by light in vacuum during a time interval of $1/299792458$ of a second   So when an atom in a faraway (redshifted) galaxy is X meters away , then due to the expansion of space, after sometime it is more than X meters away.
I would suggest that in physics, motion is a change in position of an object with respect to time. Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame.
Therefore we say quite rightly that relative to the earth a faraway galaxy with a redshift it has a motion (away from us)
Now a bubble of space with its center at the center of an atom in the faraway galaxy and where the atom is at rest locally this bubble had its center also at some time point X meters away from the earth.
As the atom is locally at rest, i.e it is not moving locally in space, then the bubble of space  which contains the atom is also locally at rest, therefore there is no movement of the atom relative to the bubble so the center of the bubble will also be more than X meters away  after some arbitrary time later.
Therefore the bubble of space with its center at the center of an atom in a faraway galaxy has a motion relative to the earth.
Therefore I would conclude that an arbitrary bubble of space can have a motion relative to an observer. 
As an analogy its like a 2 dimensional being living on a rubber measuring stick which is being stretched. The ends of the rubber measuring stick are moving relative to each other whilst the expansion occurs.


*

*Can anyone explain what is wrong with this reasoning ?

 A: What you have concluded is that a coordinate system centred on the atom, and in which the atom is at rest at the origin, would be in motion relative to our coordinate system here on Earth. But this proves only that the particular coordinate systems you've chosen can have a relative velocity. If we chose to use comoving coordinates instead, then we, the atom and indeed the galaxy X would all be stationary.
As I said in a comment to your previous question, spacetime isn't an object and it is meaningless to ask whether it is moving on not. However coordinate systems can be in relative motion, and indeed in relative acceleration.
A: Space is not nothing. You can "condition" it such that spacetime is curved, forming a gravitational field. See Einstein saying space is neither homogenous nor isotropic and not "empty" in his 1920 Leyden Address. Also see him talking about electromagnetic and gravitational fields in 1929. Note this: "It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds". According to Einstein, a field is a state of space. The Robert Laughlin quote here is also worth noting: 
It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed [..] The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum..."

Can such an arbitrary bubble of space have a motion relative to an observer on earth?

Yes of course. Space isn't nothing, and the universe is expanding. Space is expanding. And space isn't nothing. Look at the stress-energy-momentum tensor. It "describes the density and flux of energy and momentum in spacetime". See that energy-pressure-diagonal? And the shear stress term? 
Public domain image by  Maschen, based on an image by created by Bamse see Wikipedia 
It's kind of elastic. Google it. 

My reasoning: We have chosen the meter as the length of the path traveled by light in vacuum during a time interval of 1/299792458  of a second So when an atom in a faraway (redshifted) galaxy is X meters away , then due to the expansion of space, after sometime it is more than X meters away. I would suggest that in physics, motion is a change in position of an object with respect to time. Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame. Therefore we say quite rightly that relative to the earth a faraway galaxy with a redshift it has a motion (away from us) Now a bubble of space with its center at the center of an atom in the faraway galaxy and where the atom is at rest locally this bubble had its center also at some time point X meters away from the earth.

Your reasoning is correct. 

As the atom is locally at rest, i.e it is not moving locally in space, then the bubble of space which contains the atom is also locally at rest, therefore there is no movement of the atom relative to the bubble so the center of the bubble will also be more than X meters away after some arbitrary time later. Therefore the bubble of space with its center at the center of an atom in a faraway galaxy has a motion relative to the earth. Therefore I would conclude that an arbitrary bubble of space can have a motion relative to an observer. As an analogy its like a 2 dimensional being living on a rubber measuring stick which is being stretched. The ends of the rubber measuring stick are moving relative to each other whilst the expansion occurs.

As above. 

Can anyone explain what is wrong with this reasoning?

No. Einstein said "the idea of motion may not be applied to it". But that was before we knew the universe was expanding. He should have predicted that. Those galaxies aren't moving apart for nothing.  
