The puzzle of time

Now is not an objective phenomenon, it is not even a material phenomenon.

We can refer to moments in time. The physicist speaks of time t, the journalist specifies a time by referring to a calendar. But what does it mean for a time to be now?

Objectively, now has no meaning. Suppose I look at my watch, I see it is noon--we'll cal it time t₁. I write down a description of all of the relevant details. Five minutes later I look at my watch, time t₂, again I write down a description. Every fact that I have written down about time t₁ is still true about time t₁, even though those facts may not all apply to time t₂, they still apply to time t₁. So, if those facts are still true about t₁, then why is now no longer at time t₁?

Let's examine this puzzle a little more carefully. What causes any particular time to be now? In general, a phenomenon can have multiple causes. When I flip a light switch, the light (usually) comes on. I may begin to believe that my flipping the switch causes the light to come on. But is this the only cause? One day I may flip the switch and find that the light does not come on. Since like causes should have like results, I infer that the light coming on must have more causes than the position of the light switch alone. I may not know what these other causes are, although in the case of the light I can list many of them (there must be a continuous wire from the power source to the switch, and from the switch to the lamp, the power source must be operational, no blown circuit breakers, etc.). The point is that if I catalog a list of causes, and then notice that identical causes do not produce identical effects, then I know that my catalog of causes is incomplete.

So consider a maximal catalog of causes in the objective universe, a world book containing all objective information about every point in space-time, from the origin of the universe until its end. This world book will catalog my looking at my watch at time t₁ and saying It is now noon. It will catalog my looking at my watch at time t₂ and saying it is now 12:05. Objectively, there is no conundrum at all--clearly I am allowed to make those two statements at those two different times, but, subjectively, something in the universe changed.

That is, from the objective standpoint of the world book, the situation at time t₁ exists and does not vary depending on my perspective. However, as a sentient being--a time traveler (in the usual sense of moving forward through time in the usual way)--I realize that my subjective perspective on the universe has changed. Nothing objective has changed, only this subjective perspective. Clearly then, the perspective is not objective, since there is no objective statement about a point in time whose truth depends on that perspective.

An analogy

Consider the act of reading a book. I might, at some time, look at the page numbers. I might say I am reading page 200, I could even write it in the margin, let's call that set of facts p₁. After reading a bit more, I might say I am on page 205, I could call that p₂. It would be no trick for the author to have written those margin notes. Those are the objective trappings of my journey through the pages of the book. Indeed, most books are published with page numbers. The descriptions associated with the various pages do not change, depending on whether we are reading them or not. But, as readers, we do have a subjective perspective that changes.

A mistake

The mistake that the concept of now arises from material causes, is the same kind of mistake a reader might make if he decided that his subjective perspective on a book were caused by the book itself.

Subjectively, we know that, given the universe, we have a subjective perspective on time, we call now. I'll write that as Now(U), where U refers to the entire collection of facts about the Universe, throughout its breadth of space and time. What point in time does this select? It is just one point in time--I am only aware of one point in time being now. The problem is that on one occasion the function evaluates to t₁, on another occasion, to t₂. Note, that it only begs the question to say that it evaluates to t₁ at time t₁ and to t₂ at time t₂. To say that is to insist that the function must be written Now(U, t₁) in the first case and as Now(U, t₂) in the second case--in other words that the quality of now-ness is independent of U. More generally, however, we can say that we must write Now(U, x₁) and Now(U, x₂) where x₁ and x₂ are independent of U. In either case, we have shown that the passage of time is independent of the objective aspects of the universe.

To put this in terms of the book analogy, suppose consider the page we are on as Page(Book). This doesn't work because this can, on one occasion evaluate to page p₁ and on another occasion evaluate to page p₂. To say that it evaluates to page p₁ when we are reading page p₁ is to insist that the function in that case must be written Page(Book, p₁), in other words to accept that the page we are on enters independently of the book itself.

The arrow of time

Note that the above discussion is not that closely related to the question of the arrow of time. That problem is concerned only with why physics is asymmetric with respect to time. This approaches a subjective question about time when the discussion gets to such things as why do we remember only the past and not the future?, but the boundary into the subjective is not crossed. We have shown that in physics, the question of the location in time of our subjective perspective does not arise. The arrow of time is an objective concept, but the passing of time is not.

Time proves to be asymmetric with respect to such things as entropy increase and wave function collapse. Intuitively, maybe the irreversible increase in the entropy of statistical ensembles, in fact, arises from the implications of wave function collapse in chaotic systems.

Time travel

Given that the passage of time is not an objective concept, it is a little strange that physicists sometimes talk about time travel. Objectively, what this means is not that the subjective awareness of now moves in unexpected ways, but rather that causation can happen in unexpected ways--for example that a phenomenon might be caused by events in the future as well as in the past. The world book is invariant--at each point in space-time there are particular attributes which do not change, and objective notions of time travel relate only to whether the values of these attributes might be considered to have been caused by chains of events that bypass the normal sequences in time.

(Updated: 2004-03-29)
(Updated: 2006-09-10)
(Updated: 2009-07-08)