Does Shoemaker's thought experiment about time really work?

Question

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.

Answer 1

What troubles me the most is that it looks to me like he basically redefines time to prove something about time.

As far as we know, parts of the universe can not be frozen. The period of the revolution of the earth around the sun defines a year. We can imagine that stopping the course of the earth would cause time to stop, but what happens really ? If the earth lateral motion is stopped, it starts falling inside the sun. To keep it really still, We would need some kind of giant tractor beam, and this tractor beam's energy supply would include thermodynamic processes indicating the flow of time. If we freeze the tractor, the earth falls, again indicating the flow of time. And I won't even touch the subject of how the tractor beam itself is maintained at the same position...

It really looks like the flow of physical time, as we got to know it through the study of nature, can't really be stopped, because motion can't be stopped without inducing further motion by conservation of momentum.

Although I understand that it is the very essence of though experiments to posit something that can't be physically done, to me Shoemaker, by positing that the universe could be frozen, stealthily redefines time as something that can pass without change, and then proceed to this same conclusion.

Note that I am not saying he did it on purpose. The flaw is certainly unintentional, but he is, in my opinion, begging the question.