Assume you want to implement shared data with private modifications: As long two processes use some original data, they should access the same physical memory $($shared memory$).$ As soon as one process modifies the data, that process will get its own, private copy of the data, and the modifications are performed on that private copy, not on the shared data.

$($For example, you can implement such strategy with the MAP$\_$PRIVATE option of the mmap system call$).$