Shoemaker gives us an interesting thought experiment about time:
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 experiment, however, seems to take the flow of empty time for granted in an attempt to prove that we can posit periods of empty time and claim to know how long they are.
When all the portions stop because the periods of freeze intertwine, Shoemaker maintains that time continues to flow – I suppose because otherwise the rule of alternation would break and no portion could unblock.
But is this rule well grounded? Where there's no synchronicity it is grounded on the basis of the normal passage of time of the portions not immobilized, but when they are all frozen the implied reference seems external to these three parts (as in a hypothetical part 4) or a meta-time that continues to flow.
Let me explain better: at any moment when none of the portions is frozen, it could happen that all the portions freeze for an "indefinite time", but on the basis of this untraceable stasis no new rule could be deduced. The fact that the rule of alternation continues to work with the same rhythms even when everything is static, either it is an axiomatic assumption with no demonstrative value, or it is an unverifiable hypothesis, based on the trust in the regularity of every freezes, calculated however on the basis of a time without stasis. A rule is always hypothesized after an event, never a priori. Between every instant (defined as the smallest change) there’s infinite ‘empty time’.
EDIT: Indeed, there’s a little inductive reason to believe that the rule is preserved, the fact that the right portion is the first to restart. Anyway, the biggest problem with the experiment is that time, in science as in philosophy (and in Shoemaker's experiments itself), is a measure of the change of something. When parts of the universe are stationary one can still talk about time, because something changes, but when everything is stationary the idea itself becomes indefinable and loses meaning: to say that time passes even when A, B, and C are motionless is wrong, because there is no change that time could measure. The concept of 'empty time' whose possibility one wants to demonstrate simply has nothing temporal: it is like to posit that the word 'death' in an atheist and in a Catholic means the same thing. If you distort the concept of time from which you start, then you can no longer speak of time. It would be like saying that gravity remains the same even without objects with mass, the speed of light without photons, music without air vibrations.