I understand that a 64-bit processor can hold a 64-bit long address and that a 64-bit address can represent $2^{64}$ different values. But I don't understand why that processor can address $2^{64}$ different locations in memory at one time and thus process billions of billions of GB at a time (theoretically). 

I haven't found a satisfying answer on google. On google they just explain that a 64-bit address can represent $2^{64}$ different values and thus it equates to the processor being able to process $2^{64}$ values (or memory locations) at a single time, though I am interested in as much detail as possible regarding how exactly that looks like. 

64-bit address means for me that this address can have one of $2^{64}$ possible values and not that it can process $2^{64}$ at a time.