Can Time Exist Without Change?

The Question Raised by Shoemaker’s Thought Experiment

What is time? The apparent simplicity of this question stands in sharp contrast to the difficulty we encounter when attempting to answer it. In our everyday experience, time appears to be inseparably linked to motion and change. We recognize that time has passed because something has changed: the position of the Sun, the hands of a clock, or the arrangement of the objects around us. Yet this intuitive association between time and change is not sufficient to resolve the metaphysical question of what time really is. We may ask whether time is produced by change or, on the contrary, whether it constitutes an independent reality within which events take place. In other words, does time continue to exist when no change whatsoever occurs?

Before attempting to develop a general theory of the nature of time, the present article addresses a more limited question: can there exist a temporal interval during which absolutely no change occurs?

Many philosophers have sought to answer this question. Among them is the American philosopher Sydney Shoemaker, who, in 1969, proposed one of the best-known thought experiments against identifying time with change. His aim was to show that we can coherently conceive of the existence of time without change.

To defend this possibility, Shoemaker asks us to imagine a world divided into three distinct regions, designated A, B, and C. These regions are interconnected and inhabited by people capable of observing what happens in the others.

In this imaginary world, an anomaly occurs: at regular intervals, one of the regions becomes completely frozen for one year. During this period, no change whatsoever takes place within that region. The inhabitants of the other two regions can observe that nothing at all occurs there. Once the year has elapsed, the frozen region resumes its normal activity, and its inhabitants once again interact freely with the others. Yet the situation appears strange to them, since the remaining regions have continued to evolve while they themselves remained frozen.

These periods of suspension occur periodically in the different regions. Up to this point, however, we still do not have a case of time without change, since whenever one region is frozen, the other two remain active.

Now suppose that the suspensions follow the following pattern: region A freezes every three years, region B every four years, and region C every five years. As a result, every sixty years all three regions are simultaneously frozen for an entire year.

Shoemaker argues that we have now obtained precisely what we were looking for: a world in which there exists a period of time without change, and whose inhabitants are nevertheless able to predict that such a period has occurred.

The thought experiment therefore aims to show that we can have rational grounds for believing in the existence of a temporal interval during which absolutely no change has taken place. If this conclusion were correct, change would no longer be a necessary condition for the existence of time. Time could continue to pass even if the entire universe remained completely motionless.

Shoemaker’s argument is philosophically elegant and compels us to distinguish between two issues that should not be confused: the possibility of measuring time and the possibility that time exists.

In what follows, I shall argue that Shoemaker’s thought experiment fails to establish the existence of time without change. Even if we grant that time could exist as an ontological reality independent of our instruments of measurement, its passage would still have to introduce some real difference into the totality of what exists.

First Objection: Measuring Is Not Demonstrating Existence

The first difficulty raised by the thought experiment concerns the very duration attributed to the global suspension. As long as only one region remains frozen, its inhabitants can use the other two as reference systems. They can ask how much time has elapsed and compare their previous state with the subsequent state of the rest of the world. By contrast, when all three regions are simultaneously frozen, every physical reference by which the duration of the interval could be determined disappears. Once activity resumes, the states immediately preceding and immediately following the suspension could be connected without any intermediate process capable of establishing how much time has actually elapsed.

Shoemaker argues that, since each individual suspension has regularly lasted one year, it is reasonable to infer that the global suspension also lasts one year; in other words, our knowledge of its duration derives from past experience. Yet this previous regularity does not seem sufficient to determine the duration necessarily. In the complete absence of change, any duration would be compatible with the observable states. One could claim that one year, ten years, or even a million years had elapsed, and there would be no observable difference between these temporal assertions. This suggests that the duration attributed to the global suspension cannot be verified by any internal process within the imagined world.

Nevertheless, a distinction must be drawn between measuring a reality and demonstrating its existence. The fact that something cannot be measured does not necessarily imply that it does not exist. It would therefore be insufficient to identify time with the impossibility of measuring its intervals.

Human beings measure temporal intervals by relying on regular processes, such as the Earth’s rotation, the oscillation of a pendulum, or atomic transitions. None of these processes is time itself; rather, they are changes that we use as standards for comparing other changes.

Shoemaker could argue that even if every clock ceased to function and every possibility of measuring duration disappeared, time would nevertheless continue to exist. Let us provisionally grant this possibility. Let us suppose that time is an independent ontological reality, a real structure that exists even if no human being perceives it and even if no physical process makes it measurable.

The fundamental question then ceases to be epistemological. We are no longer asking how we know that time has elapsed, but rather what it means, ontologically, for time to have elapsed.

Let us call t_n the first moment of the simultaneous suspension of regions A, B, and C, and t_n+1 a later moment. If absolutely no change occurs between these two moments, then the total state of reality remains identical: S(t_n) = S(t_n+1).

The difficulty is then to explain on what grounds one may affirm that t_n and t_n+1 are genuinely two distinct moments. It is not enough simply to assign them different names, for what must be justified is precisely the existence of a real plurality of moments, rather than the mere conceptual duplication of one and the same configuration.

One might reply that t_n and t_n+1 occupy different positions within a substantive conception of time. Just as two points in space may be distinct despite possessing identical qualitative properties, two moments might likewise be numerically distinct solely by virtue of occupying different temporal positions.

The Real Question Is Ontological

I now ask what makes reality first be at t_n and then at t_n+1.

The difficulty becomes particularly evident when the suspension must come to an end. For the three regions to resume their activity after one year, there must be some difference between the beginning, the course, and the end of the suspension. There must be something that accounts for the fact that reactivation has not yet occurred at t_n, but does occur at t_n+1.

If there exists a process, a property, or a structure that distinguishes these two moments and determines when activity is to resume, then there must also exist change in the totality of reality itself. Change would not have disappeared; it would merely have been displaced into the temporal structure itself.

If, on the contrary, nothing changes in any respect whatsoever, then there is no ground on which the suspension could come to an end. The suspended state contains no new condition capable of bringing about its own termination.

From all that has been said, it is neither necessary to identify time with its measurement nor to offer, at this stage, a complete theory of its nature. It is sufficient to uphold the following condition:

For there to be a genuine passage of time, there must exist some ontological difference between moments; that is, reality as a whole must undergo change.

At this point, Shoemaker might reply that two moments can be distinct even though the content of the world remains exactly the same.

Such a reply, however, leads to a dilemma.

Either the difference between t_n and t_n+1 constitutes a real fact. In that case, this difference belongs to the totality of reality, and the corresponding states are therefore no longer ontologically identical. Reality at t_n possesses the property of being located at t_n, whereas reality at t_n+1 possesses the property of being located at t_n+1.

Or else this temporal location is not part of reality. In that case, there exists no ontological fact capable of grounding the distinction between the two moments. t_n and t_n+1 would then be nothing more than two labels applied to one and the same configuration, perfectly identical with itself. The purported marks of differentiation would therefore lack any real foundation.

Shoemaker’s thought experiment may represent a series of moments independent of change, but it does not demonstrate that this series constitutes a genuine passage of time. In reality, it presupposes a substantive conception of time and then relies on that very presupposition to conclude that time can exist without change.