Like water is displaced by a solid object.
There's no particular reason to believe that there is such a thing as the fabric of space. It's not part of the math, no experiment has ever been devised that might give a different result depending on whether it existed or not, and there's nothing that is better explained if it does exist than if it doesn't.
You'll see the word "fabric" used sometimes as a metaphor or analogy in non-mathematical descriptions of General Relativity, but that's just a metaphor; no one is saying that there's a real fabric out there that could be displaced.
But space can be warped, bent and twisted by gravity so it has physical properties and dimensions.
What list of properties must something have to be considered a "fabric"?
Spacetime can be flat or curved so it could be said to have geometric properties, and by the EFE it could be said to have stress-energy.
It doesn't have kinematic properties like position or velocity.
There was another thread on this topic a while back: https://www.physicsforums.com/showthread.php?t=716306
It is SPACETIME that is affected by the presence of mass, not just space. In SR and GR, they are coupled together. This is why trying to picture this as a "fabric" is inaccurate. An analogy can only go so far before it becomes nonsensical if one tries to take it seriously.
Maybe I shouldn't take those space documentaries hosted by Morgan Freeman so literally.
was there space before the big bang?
I tend to think of mass not only influencing space, but creating it. so at the big bang did space race out ahead of mass or just ride along with it?
May be "frame dragging" can be considered as an example of a situation where something similar to what the OP describes is actually happening.
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