In Lamport's paper, Time, Clocks, and the ordering of Events in a Distributed System he says that the converse of the clock condition does not hold and if it did, we could expect concurrent events to occur at the same time. I am not sure how he arrives at this conclusion.
The Clock Condition is:
For any events a, b in a distributed system: if a -> b then C(a) < C(b).
The converse does not hold: if C(a) < C(b) then a -> b.
Where C(n) assigns a logical clock number to any event in the system. Logical clock numbers monotonically increasing values for each process in the system and two conditions hold in order for partial orderings given that the clock condition is true:
if a and b are both events in a process P_i and a comes before b, then C_i(a) < C_i(b)
if a is a sending event in P_i and b is a receiving event in P_j then C_i(a) < C_j(b).
Intuitively I can see why the converse does not hold. It is possible in the system of logical clocks that C(a) < C(b) when we do not have a partial ordering that guarantees the relation a -> b. But I have no clue why the converse being true would imply that any two concurrent events occur at the same time.