Opposite directions

What if they rotate?

 

They could be. But they can still rotate. Imagine two blocks stuck together. The system rotates about its center. So, one block goes left while the other goes right. (Momentarily.)

What are you getting at with this question? (I don't see any obvious physics here.)

 

I would say no, at least macroscopically.

That's a much better example (of two things with no space between them moving in opposite directions) than my rotating object example! So I guess you answered your own question. Another example would be two things sliding across each other.

 

I'm not sure what kind of answer you are looking for. It seems like you are hanging alot on the meaning of "empty space". You slide a block of wood across a table. Is there "empty space" between the wood and the table? Macroscopically, I'd say no; but microscopically, there's plenty of empty space. After all, most things are mainly "empty" space. The only real "contact" between the surfaces is at the surface irregularities. I'm not seeing the issue. (And I certainly don't see the impact on modern day physics!)