On a system with paging, a process cannot access memory that it does not own. Why? How could the operating system allow access to other memory?

Explanation:

On a system with paging, a process cannot access memory that it does not own because the page is not in its page table also the operating system controls the contents of the table,therefore it limits a process of accessing to only the physical pages allocated to the process.

The operating system could allow access to other memory by allowing entries for non-process memory to be added to the process page table.that way two processes that needs to exchange  data can efficiently do that . i.e creating a very efficient inter-process communication