Virtual addressing MMU, where are they stored

I know there are those 2 types of memory virtual and physical, and MMU mapping between them, but WHAT I can't understand is WHERE are stored those virtual addresses if they are "virtual". Admitting I have 1 process and he has something to read at his virtual address 0x00000004 then the MMU is going to map this virtual address to 0xSomeWhere in the real physical address. What I want to know is WHERE is this information stored --> 0x00000004 <-- because somewhere there MUST be those bits 00000000000000000000000000000100.

Admitting I have another similar process and he also has an instruction to read at his virtual address 0x00000004, where is this one? How are separated the 2 processes?

Just like array indexes, virtual addresses are usually¹ not stored anywhere; they're implicit. The virtual address is used as a index into the page table to look up the physical address.

_{¹It actually depends on the MMU implementation. Some, such the a PowerPC/Power architecture use a hashing scheme that does involve actually storing virtual addresses in the page table instead of physical addresses}