How are same virtual address for different processes mapped to different physical addresses

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I have taken a course about Operating System design and concept and now I am trying to study Linux kernel thoroughly. I have a question that I cannot get rid of. In modern operating systems each process has own virtual address space(VAS) (eg, 0 to 2^32-1 in 32-bit systems). This provides many advantages. But in the implementation I am confused at some points. Let me explain it by giving an example:

Let's say we have two processes p1, p2; p1 and p2 have their own VASes. An address 0x023f4a54 is mapped to different physical addresses(PA), how can it be? How is done this translation in this manner. I mean I know translation mechanism but I cannot understand that same address is mapped to different physical address when it comes different processes' address space.

0x023f4a54 in p1's VAS => PA 0x12321321
0x023f4a54 in p2's VAS => PA 0x23af2341 # (random addresses)
virtual-address-space kernel linux-kernel
6 Answers

I think it is important to keep in mind that each process has its own set of page tables. I had hard times understanding this as well when I was thinking that there is a single page table for the whole system.

When specific process refers to its page table and tries to access the page that has not yet been mapped to a page frame, OS allocates a different piece of physical memory for that specific process and maps it to the virtual address.

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