In his argument that time intervals can exist without change, Shoemaker gives us an interesting thought experiment. For those unfamiliar, here it is:
Assume that an entire universe is divided into three parts -- A, B, and C. Every 3 years, everything in A freezes for a year. Every 4, everything in B freezes for a year, and every 5 for C. After 3 years, we know that region A is frozen because B and C observe that nothing is changing in A (the same applies when B is frozen, when C is frozen, when A and B are frozen, etc). Each region is unfrozen after one year. This cycle continues indefinitely. After 60 years, however, A, B, and C freeze at the same time. Because the regions became unfrozen in the past, we can assume using induction that A, B, and C will unfreeze, and that time has passed without change.
The part of this argument I am concerned with is "After 3 years, we know that region A is frozen because B and C observe that nothing is changing in A (the same applies when B is frozen, when C is frozen, when A and B are frozen, etc)." How can B and C observe a frozen A if nothing is changing in A? In order to observe something, at the very least a single photon must travel from region B to region A and back to B in order for B to observe A. However, this can't happen because nothing is changing in A. Has this created serious problems for Shoemaker's argument, and has any philosopher taken note of this problem and developed it into an argument?