ILLUSION AND REALITY
An Unconventional But Constructive Look At The Fundamental Nature Of Time
J. C. N. Smith
The task is not so much to see what no one yet has seen,
but rather to think what no one yet has thought about that which
We have to learn how to use our words. It's a fantastic thing -- we humans are so easily trapped in our own words. The word time, for instance -- we run into puzzles about the concept of time and then we say, oh, what a terrible thing. We don't realize we're the source of the puzzle because we invented the word ....
John Archibald Wheeler
One of the primary reasons that the fundamental nature of time has remained such a persistent conundrum is, I believe, that we have never properly defined exactly what it is that we’re talking about when we use the word “time.” In what follows, I offer what I believe are some constructive steps toward correcting this omission.
We commonly use the word “time” to refer to what are, in reality, two somewhat different, albeit closely related, notions: the notion of “a particular time,” and the notion of “a measure of elapsed time.” Let us examine each of these and the relationship between them.
Correctly understanding what we mean when we refer to “a particular time” is the key to a clearer understanding of the fundamental nature of time. Perhaps somewhat surprisingly, this concept is not nearly so difficult to comprehend as we may have been led to believe.
Let us begin with a simple example. Search your memory until you come across a vivid recollection of some particular time in the past that has a special significance for you, preferably some pleasant occasion, a birthday perhaps, or some other noteworthy event.
Now, ask yourself what it is about that particular time that “defines” it. In other words, what is it, exactly, that sets that particular time apart from all other particular times and makes it uniquely identifiable?
Is it the date on the calendar? That certainly would be one part of it. But is that the only thing that defines it? Is that even the most important thing? I suspect not. If the particular time you are thinking about is a birthday, then the date on the calendar would allow you to determine how many times the Earth had revolved around the sun since you were born, and hence your age. But this cosmic detail probably is not the answer either.
Upon some reflection, you may conclude that it was a combination of many things which made that particular time memorable; perhaps these would include the friends with whom you shared the occasion, perhaps some special location where you and your friends gathered to celebrate.
Let me suggest that a constructive way to think about this is to posit the notion that the particular time you are thinking about is best defined, in the final analysis, by describing the particular configuration of the universe that corresponds with that time.
“Ah, yes, of course,” you may say, “why didn’t I think of that? All one need do to define a particular time is simply to jot down on a slip of paper the precise configuration of the entire universe which corresponds with, and which in fact defines, that particular time!”
Well, not exactly. Unfortunately, there are a few practical considerations which stand in the way of that approach, not the least of which is the fact that we cannot possibly have complete knowledge about the configuration of the universe. As many writers on this topic have eloquently noted, every observer of the universe will have a different perception of its configuration.
Moreover, because the speed of light is finite, all of our perceptions about the configuration of the universe are essentially yesterday’s news; they are out of date. The star that we observe twinkling in the night sky may have exploded spectacularly hundreds of years ago and we simply have not yet received the word. Even the light arriving at our eyes from across the room or from this page is “out of date” by an infinitesimal amount.
Does this then imply that that it is useless to think about or to talk about the configuration of the universe? I would maintain that no, it is not useless to do so. The analogy that comes to mind is that of the several blind persons who, having never previously been at all acquainted with elephants, are positioned at various fixed locations around an elephant and who are each then given the task of examining the portion of the elephant within his or her reach and then finally providing a description of the elephant.
The fact that their descriptions may all turn out to be vastly different is not a compelling reason to believe that the elephant does not exist or that it does not have a real configuration. The universe is our “elephant;” its configuration is elusive and constantly evolving, but the fact that it is intrinsically impossible for us to know its total configuration does not mean that a configuration does not exist.
Nevertheless, given these serious limitations on our potential knowledge about the universe, mustn’t we then at least concede the impossibility of ever defining a particular time in terms of a particular configuration of the universe? Perhaps surprisingly, I think not. To understand why, it may help to think about what we typically mean when we use the phrase “a particular time.”
As this concept, and terminology, typically are used in everyday parlance, particular times are defined very imprecisely (relative to the unattainable ideal of describing them in terms of the corresponding configuration of the entire universe) and yet they still retain immense practical value.
Our knowledge about events that have shaped human destiny, i.e., our knowledge about untold numbers of wars, revolutions, and a scattering of scientific and technological milestones, for example, comes from recorded descriptions of these events and the actors who participated in them. These events and actors represent relatively small bits and pieces of larger configurations of the universe. And although the events all took place in the context of specific, unique backdrops consisting of infinitely vast, complex, and intrinsically unknowable configurations of the universe, these broader configurations typically are not central to what is, for us, the crux of these particular times. Consequently, we simply choose to ignore these larger backdrops. And it works. It seems that particular times can be defined as loosely or as precisely as we choose and still retain some varying degree of utility.
Let us look at an example. If we are thinking about a particular configuration of the universe which includes an ensemble of atoms known as Julius Caesar, and especially if that ensemble of atoms functions as the leader of other ensembles of atoms known as the Roman Empire, then we can be reasonably confident that the particular time we are thinking about is one we customarily refer to as the 1st Century BCE. Because of the relatively imprecise way in which we implicitly have defined the 1st Century BCE, it is not essential that we know anything about the configuration of any far-flung portions of the universe in order to draw this inference.
We can turn this example around and make what logically is a much stronger assertion. We can say with absolute assurance that if there is no ensemble of atoms known as Julius Caesar functioning as the leader of a Roman Empire anywhere on our planet, then it definitely is not the particular time we refer to as March 16th, 44 BCE, for example. Similarly, if objects located on the Earth were to include dinosaurs or steam locomotives or laptop computers we could again say with confidence that the corresponding time is not the 1st Century BCE, because these things are not part of the configuration of the universe that defines the 1st Century BCE.
A key point here is the idea that what really “defines” a particular time is not so much a date written on a calendar or the reading of a clock, but rather a configuration, regardless of how loosely defined, of some known portion of the universe.
Despite being relative newcomers on the historical scene, calendars and clocks rapidly have assumed an extremely important role in our lives, and this is true precisely because they serve the powerful and useful function of providing a concise shorthand for communicating information about configurations of the universe.
Simply by saying that I plan to talk about the 1st Century BCE, for example, I avoid the tedious necessity of having to explain that I plan to talk about the time long after dinosaurs disappeared from the Earth, and after the time of cavemen but before the advent of steam locomotives and laptop computers, and, oh, yes, maybe this will help pin it down; it was about the time when the Roman Legions were under the command of Julius Caesar. Knowing even an approximate date allows us to make some important inferences about the corresponding configuration, albeit perhaps somewhat loosely defined, of at least some relatively small portion of the universe.
Clocks perform a function analogous to that of calendars, but on a finer scale. Knowing the time of day can provide a great deal of information about the rough configuration of several portions of the universe. At 6:00 AM the sun will be rising on the eastern horizon and a flight should be departing Dulles Airport headed for Los Angeles, at 3:00 PM a movie will begin at the local cinema, at 5:00 PM the freeway will be clogged. We joke ruefully about needing a calendar rather than a clock to measure and describe our wait in traffic.
The power of calendars, and perhaps even more so of clocks, to simplify and organize our lives has proven to be so great that it has tended to blind us to the underlying fact that the fundamental role of these devices is to provide a shorthand way of communicating information about configurations of the universe.
Clocks, in particular, have taken on an importance that would be difficult to overestimate, often bordering on a form of tyranny over our lives. We are driven to create clocks that are ever more precise and accurate, and not without good reason; precise, accurate clocks serve as far more powerful tools than imprecise, inaccurate clocks. We have even gone so far as to elevate the “product” of our clocks, this thing we have named time, to the status of an independent, fundamental unit of the physical universe.
Unfortunately, I fear that we have allowed ourselves to be tricked by our use of language into believing in the reality of a chimera. As the first step in this process of self-delusion, (a step which is, in and of itself, innocent and logical enough), we began equating various imperfectly-known configurations of the universe with what we termed "particular times." Given all that has gone before in this essay, I can have no quarrel with this first step, per se. Indeed, taking this step is so natural that the practice became a universally accepted convention of thought and speech and, as such, it gradually became essentially invisible to conscious thought. We spoke of "times changing," meaning that the configuration of the universe changes. So far, so good.
With the invention of the calendar and clock, however, things began to go rather badly awry, in my opinion. Now for the first time we could talk about our calendars and clocks "marking the passage of time," or "measuring the passage of time," or, much more insidiously, we could talk about them "measuring time." Ergo, it could be reasoned or assumed without giving it a great deal of thought, that "time" must be something real and measurable, much as distance and mass are measurable, in and of itself, separate and distinct from the broader context of particular times (i.e., configurations of the universe), from whence it sprang.
Unfortunately, we are still living with the ripple effects of this linguistic slight of hand. I would submit that our continued uncritical acceptance of this linguistic legerdemain even as recently as today makes us complicit in the undoing (or at least in the unnecessary complication) of modern physics, an undoing which was thus set in motion even before the advent of physics as a science. This is immensely ironic, of course, given that many of the early successes of physics came about precisely because the early practitioners of physics skillfully employed the very same conventional view of time which I am now criticizing as being flawed. 
Having thus levied this criticism of our generally accepted current way of thinking about time, I would like to build on the preceding observations to suggest what I hope might be a more constructive way to think about and to define time.
As a way to proceed, let us agree, at least for the sake of argument, that when we refer to a particular time we are in fact referring to some particular, more or less loosely defined, configuration of some known portion of the universe. This will be a good starting point. Next, I would like to refine this starting point and propose the following, somewhat more formal and rigorous definition: a particular time is identically equivalent to, and is completely defined by, and only by, a particular configuration of the universe. This definition can lead, I believe, to some rather profound, powerful, and falsifiable conclusions. These will be addressed in concluding our essay.
It is important at the outset to recognize and, insofar as possible, to “internalize” the notion that the configuration of the universe does not change as a result of time advancing; rather, time changes (as we say, “advances”) because the configuration of the universe changes. The importance of grasping this subtle, admittedly perhaps counterintuitive, distinction can hardly be overstated in terms of furthering our understanding of time. Failure fully to comprehend and appreciate it has led, I believe, to many unfortunate intellectual detours and cul-de-sacs over the course of history. The evolution of the physical universe is what we perceive as the flow of time.  If the configuration of the universe did not change there would be no flow of time.
If then, as we have proposed, a particular time is identically equivalent to, and is completely defined by, and only by, a particular configuration of the universe, it follows logically that time changes if, and only if, the configuration of the universe changes.
Now, I would propose that the configuration of the universe changes if, and only if, some portion of the universe is displaced relative to some other portion. Therefore, I believe it follows that if we are to observe and measure a change in the configuration of the universe (and, hence, a change from one particular time to another), we must observe and measure a displacement of some portion of the universe relative to some other portion.
But displacements are measured, perhaps not surprisingly, in units of displacement, i.e., length. This strongly suggests, I believe, that the units we customarily use to measure elapsed time, i.e., our traditional units of time, are, in fact, emergent, or derivative units rather than independent, fundamental units.
The late Nobel Laureate Richard Feynman was fond of using what he called the "trick" of substituting units of length in place of units of time as a way to simplify his equations. For example, in his popular book Six Not-So-Easy Pieces he wrote, "... nature is telling us that time and space are equivalent; time becomes space; they should be measured in the same units.” [Feynman's italics.] I would submit that Feynman's "trick" was no trick at all, but rather an accurate portrayal of reality. 
Continuing along this line of thought, there is a much-discussed (in the world of physics at any rate) equation known as the Wheeler-DeWitt equation (named after the physicists John Wheeler and Bryce DeWitt). Having arisen during attempts to merge general relativity and quantum mechanics, this equation has puzzled physicists because it rather oddly lacks a time variable. I would suggest that this lack of a time variable may once again point toward the idea that time is an emergent concept rather than an independent, fundamental building block of nature.
In what is perhaps an even more telling observation, if we substitute units of length where units of time currently appear in the mathematical definition of energy we find that the definition collapses to a simple statement that mass equals energy. In essence, our proposed definition of time allows us, and in fact requires us, to “predict” the equivalence of mass and energy.
While the dramatic impact of this bold and falsifiable “prediction” has been immeasurably softened by the fact that Einstein made the same prediction, subsequently borne out by experiment, roughly a century ago, it is nonetheless noteworthy that we could arrive at this same “prediction” without the benefit of input from Einstein’s impressive theories.
I am not suggesting, of course, that as a result of these brief discussions we should all rush out immediately to our nearest hardware stores to exchange our clocks and wristwatches for tape measures. Units of time have long served, and will long continue to serve, a valuable practical purpose. Nevertheless, I believe that the mindless use of these customary units of time in physics (mindless in the sense of accepting these units at face value rather than subjecting them to more rigorous critical scrutiny in terms of understanding their origins and underlying meaning) has been a serious impediment to progress in solving many of the riddles that currently abound in physics. A fresh look at these matters is long overdue.
It is my hope that the concept of time advanced in this essay will provide the germ for additional thinking on this topic and that it will thereby open the door to other falsifiable predictions, at least some of which will prove to be not only new but also of value in furthering our understanding of the universe.
J. C. N. Smith
1. In his book The Trouble With Physics, Lee Smolin wrote, "More and more, I have the feeling that quantum theory and general relativity are both deeply wrong about the nature of time. It is not enough to combine them. There is a deeper problem, perhaps going back to the beginning of physics." (Lee Smolin, The Trouble With Physics, p. 256) I agree with Smolin wholeheartedly, and I speculate that the problem to which he alludes may have arisen in a seemingly innocent manner such as that described here.
2. If what we perceive as the flow of time is, in reality, nothing more and nothing less than the evolution of the physical universe (an evolution which is governed by rules which we strive to understand and which we refer to as the laws of physics), then is it possible for there not to be a causal arrow of time?
3. If the view of time presented in this essay is correct, then the speed of light c is seen to be a unit-less or dimensionless ratio, leaving Newton's gravitational constant G (with units of meters/kilogram) and Planck's constant h (with units of kilograms x meters) as the only remaining intrinsically dimensional constants of nature.
For further discussion please see:
Toward a Helpful Paradigm for the Nature of Time ( http://sites.google.com/site/smithjcnparadigm/ ),
On the Impossibility of Time Travel ( http://www.fqxi.org/data/essay-contest-files/Smith_IOTT6.cwk.pdf ), and
Rethinking a Key Assumption About the Nature of Time ( http://www.fqxi.org/data/essay-contest-files/Smith_Rethinking_a_Key_Assu.pdf )