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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.

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    1. Yes, it is fallacious, at least if it claims to prove--as it seems to--that time doesn't stop when there is no change.But it is clever! It works to an extent if we assume what we all assume by default, although only to an extent because while the reasoning is inductively legitimate, it is not deductively conclusive since it remains a possibility that time does stop when A, B and C all freeze together. -- 2. The rule is inferred only inductively, but correctly, from past experience. A, B and C each have their own periodicity, and the common freeze can be predicted. Mar 14, 2020 at 19:29
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    A thought experiment is a hypothetical setup, it can not be right or wrong. A conclusion derived from its analysis can be wrong, but your suggested conclusion isn't Shoemaker's. He does not purport to "prove time", but to show that, as SEP puts it, "it would make perfect sense to posit periods of empty time, and even to claim to know just how long those periods are". A theory of time "freezing over" is coherent, and not only compatible with observations, but also predictive. Therefore, it is a legitimate theory to adopt.
    – Conifold
    Mar 14, 2020 at 21:24
  • I will make more definite my claim, but I meant that it has no sense to posit periods of empty time and claim to know how long they are. Mar 14, 2020 at 21:42
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    That the alternation continues when everything is static is a hypothesis of the same sort as the hypothesis that desks and chairs do not disappear when we look away. Its verifiability and "demonstrative value" are moot because they invoke a wrong standard - we can not "prove" anything about empirical matters. The relevant standard is whether it is part of a simple theory that predicts observations. And it does, so it makes all the sense it needs to. We do not need to disprove every unfalsifiable skeptical "it could happen" to adopt a theory that says it doesn't.
    – Conifold
    Mar 15, 2020 at 0:09
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    Shoemaker gets an A+ from me Oct 20, 2023 at 10:18

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Thought experiments can be usefully applied in one of two ways, namely:

  1. Where you assume the laws of physics are true and consider what their consequences would be in circumstances that are allowed by them in principle but hard to realise.

  2. Where you waive one or more of the laws of physics to consider the hypothetical consequences.

What you can't do, is to arrive at a conclusion having waived the laws of physics and then assume it applies in the real world where the laws of physics are not waived.

The thought experiment described in the question is full of holes. You can't, even in principle, freeze part of the Universe. Quite apart from anything else, the 'frozen' part would be traversed by radiation from its unfrozen neighbours. Nor can you freeze a part for a fixed period of time, since proper time for any object depends on the local curvature of spacetime, so the idea of a fixed period doesn't make sense. And even if it did, there would have to be something keeping track of time to trigger the unfreezing at the appropriate point. However, leaving all those objections aside, even if you freeze particles in space they continue to coast along world lines in time. If you waive that by saying, what if you could stop them from moving along world lines, then you have entered a what if fantasy world in which whatever conclusions your draw cannot illuminate reality because they are not based on it.

IMHO Shoemaker's conclusion is correct in the sense that even if all the particles in a region of the Universe were frozen in space, they would continue to follow a trajectory in time. There would be no way of measuring time without a device that is capable of registering change, but the does not invalidate time conceptually in physics.

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  • 3. The XKCD "What If" way.
    – Scott Rowe
    Oct 20, 2023 at 16:51
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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.

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It seems these discussions of inevitably bring up time's arrow and its inexplicable link to entropy. At times when A, B and C—which, among them, comprise the entire universe so that there is nothing that can be said to be outside them—are all frozen in a state of changelessness (which, is, as @armand points out, likely impossible, but this is a thought experiment), then entropy stops as well. At any moment during this period, it is impossible to determine in which direction time flows—or at least it would be if there were anything left unfrozen that could be making such observations, which as we have seen, there is not.

However, once the frozen year was over, all observers would be in play again, and would presumably agree that time flows in the direction of increasing entropy that existed immediately before the freeze, which is the same as the direction of increasing entropy that came into existence immediately following it.

A, B and C all agree. However, there's no guarantee that, at each universal freeze, the direction of increasing entropy doesn't reverse somehow. As long as it were to reverse for all three together, there would be no observation that could be made to determine that time was now flowing in the opposite direction.

I'm not sure that this sheds much light on the question, however.

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  • I wonder if thought experiments ever fail in a Darwin Awards kind of way?
    – Scott Rowe
    Oct 20, 2023 at 16:02
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OP: 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.

In contrast to science where time is measured by the motion of matter, in the phenomenology branch of philosophy a subjective form of time is characterised as the change of one thought to another thought, and it is from this subjective position that minds collaborate to formulate the scientific form of time.

This subjective perspective is borne out by the need for A, B, or C to be unfrozen for time to be perceived. However, Shoemaker's model has a cyclic regularity, so when A, B & C all wake up at the same time after being frozen they can work out that a year had passed. Without these regular cycles, if A, B & C were all frozen no-one would be able to measure the passage of time if and when any of them became unfrozen.

The constitution of subjective time within the structure of the self is described by Heidegger, following from Kant's intuition of time ... Quoting from Kant and the Problem of Metaphysics, §34. Taft translation. (Alternate Churchill translation here.)

Time is only pure intuition to the extent that it prepares the look of succession from out of itself ... This pure intuition activates itself with the intuited which was formed in it, i.e., which was formed without the aid of experience. According to its essence, time is pure affection [as in something which affects something]* of itself. ...

As pure self-affection, time is not an acting [external]* affection that strikes a self which is at hand. Instead, as pure it forms the essence of something like self-activating. However if it belongs to the essence of the finite subject to be able to be activated as a self, then time as pure self-activation forms the essential structure of subjectivity.

* my comments

original: p. 189 Die Zeit ist nur so reine Anschauung, daß sie von sich aus den Anblick des Nacheinander vorbildet ... Diese reine Anschauung geht mit dem in ihr gebildeten Angeschauten sich selbst an, und zwar ohne Beihilfe der Erfahrung. Die Zeit ist ihrem Wesen nach reine Affektion ihrer selbst. ...

Die Zeit ist als reine Selbstaffektion nicht eine wirkende Affektion, die ein vorhandenes Selbst trifft, sondern als reine bildet sie das Wesen von so etwas wie Sich-selbst-angehen. Sofern aber zum Wesen des endlichen Subjektes gehört, als ein Selbst angegangen werden zu können, bildet die Zeit als reine Selbstaffektion die Wesensstruktur der Subjektivität.

This sketches out the phenomenological origin of time. When minds formed on this basis collaborate to formulate scientific time this still does not settle the issue of understanding cosmic time – if there is such a thing, such as time in the Big Bang or a singularity.

OP: Between every instant (defined as the smallest change) there’s infinite ‘empty time’.

Scientific time, according to the Caesium Standard, is derived from the resonant frequency of caesium atoms. This is cyclic and continuous, so there are no separate, actual instances. In contrast, an unconscious self does not experience the passage of subjective or scientific time, but upon waking they could establish that scientific time has passed and that there had been a subjective gap in the observation of scientific time.

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  • When I read the 60 year cycle, I thought of the Mayan calendar. Or the Old Testament idea of releasing all servants and cancelling all debts every 7 years. We should try that. Just a few years and my mortgage is gone!
    – Scott Rowe
    Oct 20, 2023 at 16:00
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    @ScottRowe It reminded me of The Three-Body Problem. Oct 20, 2023 at 20:35
  • I suppose. A probably unsolvable system that is about as simple as can be.
    – Scott Rowe
    Oct 20, 2023 at 22:42

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