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?


  • First, Shoemaker's argument is about time intervals that go by without changes, not about "time without change" (freezing and unfreezing explicitly presupposes change). And second, it is about mere logical possibility of such intervals. So the story about traveling photons is irrelevant, logic is not bound by the laws of physics in the particular universe we happen to inhabit. Another universe may have action at a distance and no photons. The argument does have flaws, see e.g. Altuna's analysis, but this is not one of them.
    – Conifold
    Oct 17 '19 at 23:13
  • @Conifold Ah, so I just "looked too deep" into the metaphor? I also added that the argument is about time intervals, not time itself.
    – N. Bar
    Oct 17 '19 at 23:18
  • The argument seems to adopt a naively realistic view of time and change and therefore to be deeply flawed. It is not possible to prove that time passes even when things are changing, and even change itself may be questioned as more than a mental construction. So i'd say the argument is philosophically naive and not answerable in the terms in which it is phrased. . .
    – user20253
    Oct 18 '19 at 12:11
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    @N.Bar, I actually believe the story of travelling photons is very relevant - a beautiful observation. It does not matter if one can supposedly imagine a universe without photons. one still needs to explain what they mean by "observe that nothing is changing" - maybe we can generally speak of information instead of photons - but the problem remains. It seems that if universe A is completely "frozen" then B cannot actually observe it - maybe instead they can observe something like a black hole from which no information is sent.
    – nir
    Oct 18 '19 at 14:01
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    @PeterJ, according to the wikipedia and SEP, naive realism seems to be about objects in the world - how can time and change qualify as such? they can hardly even be defined as concepts - not intelligibly anyway, and yet they are the most immediate reality. they are not a table, not a sky, not the wind - not an object at all. the term time does not even appear in the SEP article discussing naive realism.
    – nir
    Oct 18 '19 at 17:37

Even if we assume that B and C can (somehow) observer A while it's frozen, the argument doesn't hold if the A,B and C freeze a the same time, cause the moment they do they can no longer be unfrozen because they don't have any reference by which they measure how much time they has been frozen, because the measure of time (i.e the duration that change take) is measured with respect to something changing (i.e reference) either internally or externally and that's because change is a relational phenomena, so the 1 year condition for Universes to be unfrozen make no sense anymore because they can't measure this duration without any change (internal or external) that can refer to this duration of time. For more explanation, the moment they freeze at the same time no other year will passe anymore.


After 3 years, an observer looking at the time-arrested other universe will observe nothing anymore. Even photons will have stopped though they don't experience time (a photon can be seen as a particle moving with infinite sppeed in classical Newtonian spacetime where al force influences are instantaneous). So everything is litterally frozen.

This can't happen in reality of course. The mindgame is invented to show that it needs time to start time. If all three universes are frozen there is no way to make one of them go again. Unless you just let them... But then your universe is not frozen.


The thought experience is intresting however it contains a fallacy of begging the question ( it’s suppose true the things that it is trying to prove ) before i start , i think your comment is correct and they will not be able to observe what’s going on in the frozen region at least based on our physical laws but for the sake fo the argument suppose that it's possible or they will not observe anything intil the said region is unfrozen and then conclude that they were frozen for the whole year . The argument is basicually saying : 1- Region A is Frozen 2- Regions B know that region A is frozen (or don't if you prefer to stick for a non possibility of observing ) 3- Conclusioan : region A was freezed for 1 year (ater the intercation of people from the 2 region and comparing say their calendars) !

The problem is that we are trying to show that time can pass without changes however freezing regions A don’t give us any further details to what happen to time in the frozen region , the experience is assuming that because time is still passing in regions B then it should be continuing to pass in regions A despite being frozen, thus we are making the assumption that time is not related to changes from the start which was the thing we were trying to proove , we will then be led to beleive by induction that time was still passing when the 3 regions were frozen , however as long as we don’t know what happens to time in region A espicially if the region was frozen for like 30 years where people from the region A will still be young as oppose to region B where people did age ! implying that time was also froze during this period !. with that being said and in the asbsence of proof that time won’t stop locally if changes stopped we may aslo conclude that time has stopped when the 3 regions were frozen all toghter .


In the argument presented by @N._bar the universe is divided into three parts (A, B and C) and the frequency at which each of these parts becomes frozen is given. Assuming that frequency is true, we can for the time being establish this rule as a law of this universe. The law would be something like:

"Every 3 years, everything in A freezes for a year. Every 4, everything in B freezes for a year, and every 5 for C."

Where A, B and C are three distinct parts of the universe that together result in the entire extension of that universe.

Let's save this law for later. When only one or two of the parts of this universe are frozen, we can still say that there is time in the universe, because someone in the unfrozen region can measure it. The photon issue is a great observation made by @N._Bar and that can be resolved as @zakaria_larabi demonstrated. Thus, there is a way to know exactly how long a region remains frozen, as long as there is at least one non-frozen region. It is important to say that it is not correct to say something like "time is passing in region A even though there is no change, because time is passing in B", for example. If B is not frozen it can measure how long A has remained frozen, but that doesn't mean it makes sense to talk about time being in A. However, I don't think the argument made this mistake, at no point does it seem to take these as premises of the argument. The error of the argument is at the end, when it concludes by induction that even with the universe completely frozen (A, B and C frozen simultaneously) time is passing. This mistake is to consider the supposed law that we talked about at the beginning as true, but it cannot be true. When the three regions are frozen, it no longer makes sense to talk about "for a year". We cannot assume that the cases where at least one region is unfrozen is the same as the case where all regions are frozen, as stated earlier by @Deschele_Schilder.

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