Light like interval in wave function

I have read the following from what seems a reliable source:

The identification of the spacetime interval with quantum phase applies to null intervals as well, consistent with the fact that the quantum phase of a photon does not advance at all between its emission and absorption. Hence the physical significance of a null spacetime interval is that the quantum state of any system is constant along that interval.

http://mathpages.com/rr/s2-01/2-01.htm

I have two questions: (1) Is this correct; (2) if it is correct, what is the physical significance of the value of the constant? So, for instance, what would it mean were the constant equal to one?