https://writings.stephenwolfram.com/2024/10/on-the-nature-of-time/
Time is a central feature of human experience. But what actually is it? In traditional scientific accounts it’s often represented as some kind of coordinate much like space (though a coordinate that for some reason is always systematically increasing for us). But while this may be a useful mathematical description, it’s not telling us anything about what time in a sense “intrinsically is”.
We get closer as soon as we start thinking in computational terms. Because then it’s natural for us to think of successive states of the world as being computed one from the last by the progressive application of some computational rule. And this suggests that we can identify the progress of time with the “progressive doing of computation by the universe”.
But does this just mean that we are replacing a “time coordinate” with a “computational step count”? No. Because of the phenomenon of computational irreducibility. With the traditional mathematical idea of a time coordinate one typically imagines that this coordinate can be “set to any value”, and that then one can immediately calculate the state of the system at that time. But computational irreducibility implies that it’s not that easy. Because it says that there’s often essentially no better way to find what a system will do than by explicitly tracing through each step in its evolution.
In the pictures on the left there’s computational reducibility, and one can readily see what state will be after any number of steps t. But in the pictures on the right there’s (presumably) computational irreducibility, so that the only way to tell what will happen after t steps is effectively to run all those steps:
And this implies is that there’s a certain robustness to time when viewed in these computational terms. There’s no way to “jump ahead” in time; the only way to find out what will happen in the future is to go through the irreducible computational steps to get there.
There are simple idealized systems (say with purely periodic behavior) where there’s computational reducibility, and where there isn’t any robust notion of the progress of time. But the point is that—as the Principle of Computational Equivalence implies—our universe is inevitably full of computational irreducibility which in effect defines a robust notion of the progress of time.
That time is a reflection of the progress of computation in the universe is an important starting point. But it’s not the end of the story. For example, here’s an immediate issue. If we have a computational rule that determines each successive state of a system it’s at least in principle possible to know the whole future of the system. So given this why then do we have the experience of the future only “unfolding as it happens”?
It’s fundamentally because of the way we are as observers. If the underlying system is computationally irreducible, then to work out its future behavior requires an irreducible amount of computational work. But it’s a core feature of observers like us that we are computationally bounded. So we can’t do all that irreducible computational work to “know the whole future”—and instead we’re effectively stuck just doing computation alongside the system itself, never able to substantially “jump ahead”, and only able to see the future “progressively unfold”.
In essence, therefore, we experience time because of the interplay between our computational boundedness as observers, and the computational irreducibility of underlying processes in the universe. If we were not computationally bounded, we could “perceive the whole of the future in one gulp” and we wouldn’t need a notion of time at all. And if there wasn’t underlying computational irreducibility there wouldn’t be the kind of “progressive revealing of the future” that we associate with our experience of time.
A notable feature of our everyday perception of time is that it seems to “flow only in one direction”—so that for example it’s generally much easier to remember the past than to predict the future. And this is closely related to the Second Law of thermodynamics, which (as I’ve argued at length elsewhere) is once again a result of the interplay between underlying computational irreducibility and our computational boundedness. Yes, the microscopic laws of physics may be reversible (and indeed if our system is simple—and computationally reducible—enough of this reversibility may “shine through”). But the point is that computational irreducibility is in a sense a much stronger force.
Imagine that we prepare a state to have orderly structure. If its evolution is computationally irreducible then this structure will effectively be “encrypted” to the point where a computationally bounded observer can’t recognize the structure. Given underlying reversibility, the structure is in some sense inevitably “still there”—but it can’t be “accessed” by a computationally bounded observer. And as a result such an observer will perceive a definite flow from orderliness in what is prepared to disorderliness in what is observed. (In principle one might think it should be possible to set up a state that will “behave antithermodynamically”—but the point is that to do so would require predicting a computationally irreducible process, which a computationally bounded observer can’t do.)
One of the longstanding confusions about the nature of time has to do with its “mathematical similarity” to space. And indeed ever since the early days of relativity theory it’s seemed convenient to talk about “spacetime” in which notions of space and time are bundled together.
But in our Physics Project that’s not at all how things fundamentally work. At the lowest level the state of the universe is represented by a hypergraph which captures what can be thought of as the “spatial relations” between discrete “atoms of space”. Time then corresponds to the progressive rewriting of this hypergraph.
And in a sense the “atoms of time” are the elementary “rewriting events” that occur. If the “output” from one event is needed to provide “input” to another, then we can think of the first event as preceding the second event in time—and the events as being “timelike separated”. And in general we can construct a causal graph that shows the dependencies between different events.
So how does this relate to time—and spacetime? As we’ll discuss below, our everyday experience of time is that it follows a single thread. And so we tend to want to “parse” the causal graph of elementary events into a series of slices that we can view as corresponding to “successive times”. As in standard relativity theory, there typically isn’t a unique way to assign a sequence of such “simultaneity surfaces”, with the result that there are different “reference frames” in which the identifications of space and time are different.