Toward a Helpful Paradigm for the Nature of Time
Toward a Helpful Paradigm for the Nature of Time
J. C. N. Smith
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
. . . paradigms provide scientists not only with a map but also with some of the directions essential for map-making.
- - Thomas S. Kuhn
Abstract: Throughout recorded history, there has been a glaring lack of consensus regarding the nature of time. Not only is the topic a knotty one, it also has been made to appear more arcane, complex, and daunting than necessary by an insufficiently careful use of language. This paper offers definitions for what are called here “particular times” (particular configurations of the universe), as well as for “the flow of time” (the evolution of the physical universe). These lead to a new and helpful paradigm for the nature of time, as well as to falsifiable conclusions which are distinctly different from -- and mutually exclusive from -- conclusions which generally are believed to stem logically from the operational definition of time (time is that which is measured by clocks) upon which much of the edifice of physics is founded.
Uncounted reams of paper, seas of ink, and terabytes of digital data have been expended on books and essays addressing the nature of time. And yet despite all this expenditure of effort there remains an astonishing lack of anything even remotely resembling a consensus among scientists and philosophers about the fundamental nature of time. How can this be? Is the nature of time so immeasurably deep, mysterious, and impenetrable that it will forever elude our best efforts to understand it?
This essay argues that it absolutely is not the case that a clear understanding of the nature of time must forever elude our grasp and offers what I believe is a helpful paradigm aimed at improving our understanding of the nature of time. In the process, we will encounter glimpses of why the nature of time has long remained so elusive.
Anyone who has not previously been immersed in this topic might understandably be puzzled by the assertion that there is a lack of consensus regarding the nature of time. Everyone knows that time routinely is measured with amazing precision and accuracy by atomic clocks which are exemplars of scientific and technical ingenuity. So yes, in this sense of the word, which falls under the heading of horology, time is indeed well understood and is not in dispute here.
The lack of consensus arises when we begin to look more closely at the fundamental concepts regarding what it is that clocks measure. Anyone who doubts that such a lack of consensus exists might readily be convinced by performing a simple Internet search on “nature of time,” for example, or by scanning the shelves of a library or bookstore in the sections devoted to the philosophy and science of time.
There, one will find a wide and potentially bewildering array of literature which includes an astonishing variety of assertions and counter-assertions about the nature of time. For example, there are any number of books, many written by well-respected scientists, which proclaim that time travel is theoretically possible (some may even offer suggestions on how to build a time machine). And then directly adjacent to these books one may find any number of others, written by other respected scientists or philosophers, proclaiming that time travel is not possible and explaining why not.
One also will find books which debate the merits of a plethora of other time-related concepts such as presentism versus eternalism (a still-unresolved debate having origins which can be traced back to the pre-Socratic Greek philosophers Heraclitus and Parmenides). Alongside these debates will be found others regarding the virtues of endurantism versus perdurantism, along with various theories of tensed versus tenseless language and the alleged profound implications of these and other theories for science and philosophy. One also will find discussions of the pros and cons of “block time” or a “block universe” in which all times -- past, present, and future -- are equally real. Many contemporary scientists and philosophers subscribe to this block view of time and maintain that it is strongly supported by Einstein’s special theory of relativity; others, however, disagree and argue that this is not the case.
Then, just in case one were not by now sufficiently bewildered, there will be found any number of other books and essays written by respected scientists and philosophers which debate the very question of whether time is “real” or not; in other words, does such a thing as time even really exist?
This brief enumeration barely scratches the surface of the bewildering and contradictory claims and assertions that have been made, and are still being made, regarding the nature of time. The majority of these issues remain unresolved and are topics of lively and occasionally even heated modern debates.
One can imagine this situation as possibly being similar to the alternately simmering and roiling debates which must have flared between proponents of the Ptolemaic and Copernican paradigms of cosmology. The consensus which grew out of those debates, occasioning our shift in thinking from a geocentric cosmos to a heliocentric cosmos, is one of the best illustrations of the importance of paradigms, and, more specifically, the importance of paradigms which best reflect the underlying nature of reality. Did anything at all in the universe change as a result of that paradigm shift (other than the way we think about our empirical observations)? Absolutely not, but there can be no doubt that unless and until that paradigm shift occurred, progress in science would have been severely impeded.
Imagine, if you will, the difficulties that today's scientists and engineers would encounter if they were trying to plan and execute missions of interplanetary space exploration while still wedded to the Ptolemaic paradigm of cosmology. Could it be done? Perhaps, but at what cost in terms of needless complexity and difficulty?
One would hope that the difficulty and complexity of executing interplanetary space missions using the Ptolemaic paradigm might lead scientists and engineers to question whether there might be some fundamental flaw in their working paradigm. Likewise, one would hope that the persistent difficulties encountered during efforts dating back to the mid 1930s to merge general relativity and quantum mechanics, for example, might lead more than a handful of today's physicists seriously to question their working assumptions, and especially their current paradigm for the nature of time. It is my contention that a major paradigm shift is desperately needed, and long overdue, in our thinking about the nature of time. An outline for what such a paradigm shift might entail is offered below.
II. WHY THE LACK OF CONSENSUS?
The question remains open: how could a consensus regarding the nature of time possibly have eluded us for so long? The proximate cause, of course, is that this is a knotty problem. Nevertheless, the history of science is replete with knotty problems which ultimately have yielded to concerted attacks. The reasons behind the longstanding lack of consensus regarding the nature of time are complex. Perhaps symptomatic of this, there is not even an obvious consensus regarding whether the topic lies primarily within the purview of science or philosophy.
It appears to be the case that a solid majority of scientists is perfectly comfortable and satisfied with the current situation just as is, which entails their being firmly committed to a paradigm commonly referred to as the operational definition of time; i.e., time is that which is measured by clocks. Scientists dating back to Galileo have used this operational definition of time as the basis for their work, and it unquestionably has led to a long and impressive catalog of successes, including Einstein’s brilliant theories of relativity early in the 20th century. Given this record, it is understandable that many scientists might see little reason to look further for clarity regarding of the nature of time.
What appears to be a sizable minority of scientists, however, seems willing at least to entertain the possibility that there might be some value in seeking a more comprehensive understanding of the nature of time. Brian Greene, for example, acknowledging the counterintuitive nature of the mainstream scientific notion of block time, which asserts that the flow of time is illusory, wrote in his book The Fabric of the Cosmos, “Time is a subtle subject, and we are far from understanding it fully. It is possible that some insightful person will one day devise a new way of looking at time and reveal a bona fide physical foundation for a time that flows” . Block time and the theoretical possibility of time travel are among the logical consequences of the operational definition of time, which was the basis for Einstein’s theories of relativity. Einstein himself has been quoted as saying, “For those of us who believe in physics, the distinction between past, present and future is only an illusion, however tenacious this illusion may be” .
Yet other scientists, troubled by stubborn difficulties encountered during efforts dating back to as early as the 1930s to merge general relativity and quantum mechanics, have actively sought out other possible ways of thinking about the nature of time. Physicist Lee Smolin, for example, in his book The Trouble With Physics 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” . I agree with Smolin wholeheartedly, and I speculate in what follows below that the problem to which he alludes originally may have arisen in a seemingly innocuous but ultimately insidious manner. I have offered further thoughts on this in my essay Time: Illusion and Reality: An Unconventional But Constructive Look at the Fundamental Nature of Time, which is available on the Internet .
In at least some sense, the current state of affairs has begun to resemble what the late Thomas S. Kuhn described in his book The Structure of Scientific Revolutions as a “crisis state” in which “[f]ailure of existing rules is the prelude to a search for new ones” . In 2008, for example, the Foundational Questions Institute, which has as its stated mission “[to] catalyze, support, and disseminate research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality . . .,” and which boasts an impressive membership roster of prominent scientists, issued an open invitation soliciting essays on the nature of time. More than 100 essays were submitted in response.
III. WE HAVE TO LEARN HOW TO USE OUR WORDS
Another significant part of the answer to our question about the elusive nature of a consensus regarding the nature of time, I propose, is deceptively simple: it is not that the topic is so intrinsically impenetrable or beyond our understanding; rather, it is that we have not been sufficiently careful in our use of words. The late, venerable John Archibald Wheeler was, in my opinion, amazingly insightful in making the observation which serves as the opening epigraph to this essay: “We have to learn how to use our words” .
Making matters worse, I argue, the lack of sufficient care in our use of words (especially, in our use of the word time) has led to the germination and propagation of ideas about the nature of time which are far less than helpful; unfortunately, the unhelpful nature of such ideas is not always immediately obvious. In the context of various debates on the nature of time, such ideas may seem perfectly plausible.
I suggest, however, that this proliferation of unhelpful ideas has muddled deliberations on the topic, thereby generating yet further unhelpful theses in what has become a self-perpetuating loop of seemingly endless convolutions and further befuddlement. The upshot of all this is that the topic has been made to appear much more arcane, complex, and daunting than necessary. I contend that the fundamental nature of time is, in reality, amazingly simple, and, if stripped of unhelpful baggage, easily understood.
I recognize, of course, that attributing our lack of consensus regarding the nature of time to something as simple as an insufficiently careful use of words, exacerbated by a resultant proliferation of unhelpful ideas, will be viewed by many as a gross and erroneous oversimplification. After all, to say that scientists and philosophers are deeply concerned about the precise, careful use of words and language is a dramatic understatement. Nevertheless, and this latter fact not withstanding, I believe that a good case can be made to support my claim.
I hasten to add, however, that it is with deep humility and respect for those who have preceded me in pondering this topic that I offer these ideas for consideration. Clearly, if the nature of time really were as simple as I have suggested, a consensus would have been achieved long before now. If some readers are inclined at first to see this essay as yet another example of the very problem I have just described above, my only request is for a fair hearing; as with all ideas, these should stand or fall on their own merit.
Now, choose at random virtually any book or essay on the nature of time and search in it for the author’s definition of what he or she means by the word “time.” Be forewarned, however; you would be well advised not to hold your breath until you find it. Countless books have been written about the nature of time, time travel, the philosophy of time, and the whole gamut of related topics, without any effort having been made by the author to define exactly what is meant by the word time.
To be charitable, perhaps these authors simply assume, or hope, that everyone will already know what is meant by the word time without any need of further clarification, but this is exactly the problem; everyone does not know what time is. If they did, a great many of these works would not be needed. One of the most frequently repeated quotations in the literature of time is one attributed to Saint Augustine of Hippo: “What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not.” With all due respect to Saint Augustine, this simply will no longer suffice; we must do better.
No attempt will be made here to catalog all the various extant concepts and variants regarding the nature of time, whether helpful or otherwise (readers seeking more on these may refer to any number of excellent books such as Barry Dainton’s Time and Space, Second Edition , for example), but in what follows I discuss a few of the more prominent concepts.
IV. TOWARD A HELPFUL PARADIGM: THE CONCEPT OF A PARTICULAR TIME
Perhaps a good starting point for our journey toward a more helpful way of thinking about time would be to address what I believe is a noteworthy omission in the current literature of time; namely, the lack of attention to a simple concept which I will refer to as a particular time.
What do I mean by the concept of a particular time, and how might this concept be helpful in our thinking about the nature of time? Although largely overlooked in the scholarly literature of time, this concept certainly is no stranger to everyday thought and parlance. For example, I have no doubt that you will immediately understand exactly what I mean when I say that the particular time at which you are reading this sentence is different from (and necessarily later than or subsequent to) the particular time at which I am writing the sentence (assuming, of course, that you are not peeking over my shoulder as I sit at my keyboard).
This simple example merits a closer look. What is it that allows me to make such a bold assertion without the slightest fear of being misunderstood or contradicted? And why is it immediately clear to you that this assertion undoubtedly is correct? But of course you will reply that the answer to these questions is immediately obvious; there is nothing the slightest bit mysterious about it. After all, that was then and this is now, that’s yesterday’s news, it’s history now, it’s water over the dam and under the bridge, time marches on, times change, and so forth.
Yes, exactly, but might we constructively ask what deeper meaning, if any, underlies these and other similar familiar statements which allude in one way or another to what we commonly think of as the flow of time?
As a step toward answering, please ponder the following: how, exactly, does the particular time at which you are reading this sentence differ from the particular time five minutes prior to your having read it? How does it differ from the particular time one hour ago, or one day, or one year or one century ago? Correctly answering these questions will be a major milestone in our journey toward a clearer understanding of the nature of time.
If you answered that the reading of your wristwatch or your clock or your calendar would have been different at each of these particular times you will receive partial credit for a correct answer. These things certainly represent part of the answer, but are they the only part, and are they the most important part?
Upon some further reflection you might conclude (correctly, I believe) that the differences between these particular times can best be defined and characterized, in the final analysis, by describing differences in the configuration of the universe at each of these particular times. This, then, is the school solution, and some explanation is in order.
As the term is used in this essay, a particular time is defined as follows: a particular time is identically equivalent to, and is completely defined by, and only by, a particular configuration of the universe.
What do I mean by a “configuration of the universe”? I mean by this nothing more and nothing less than the physical arrangement of all the many bits and pieces which make up the universe, relative to one another.
Of course, there is absolutely no way that anyone could ever possibly know how all the many bits and pieces which make up the universe are arranged relative to one another, for a whole variety of very good and sensible reasons, but this should not be taken to mean that the universe does not have a real, albeit evolving, and intrinsically unknowable configuration. The portion of the universe about which we can have any even approximately direct knowledge, being severely circumscribed by the nature of sensory data available for us to use in constructing such knowledge is, unfortunately, vanishingly small compared to the whole.
As it turns out, however, we humans have demonstrated (somewhat amazingly, in my opinion) that we require only a modicum of incomplete information about the configuration of some relatively small but relatively well-known portion of the universe in order to make practical use of this concept. I suspect that this observation would have pleased the late Claude Shannon, the father of information theory, who developed a rigorous proof of the fact that useful information need not be drowned out by noise.
Before proceeding any farther, it may be worth asking here, as an aside, what sorts of things we can safely believe and hold to be true in our deliberations about the nature of the universe. Unfortunately, the list of these things is dismally short, in my opinion. Over the course of history, even our simplest, seemingly most intuitively obvious empirical observations have misled us badly, as in the notorious cases of our long-held, incorrect beliefs that the sun revolves around the Earth and that the Earth is flat, two incorrect beliefs which ultimately were corrected only by making, and thinking deeply about, yet other empirical observations.
Despite the obvious fallibility of our interpretations of empirical observations, however, such observations ultimately have proven, over the long run, to be our best, and perhaps ultimately our only, guide to what we may hold true about the nature of the universe. And despite the fact that empirical observations unquestionably have misled us about the nature of observed changes, I believe they have not misled us about the fact of these changes. I must respectfully disagree with those such as Julian Barbour who have argued that time and motion are both unreal . Absent motion, we would observe no change in the configuration of the universe.
With this in mind, let us return to thinking about configurations of the universe. One of our most primitive observations is that the things we can observe around us are arranged in some particular way. Perhaps our next most primitive observation is that the arrangements of the things we observe around us are not always the same; the arrangements of things relative to one another change, some of them, such as water flowing in a river, seemingly incessantly; whereas others, such as the locations of mountains, appear not to change perceptibly at all. To summarize, as sentient beings, we are able to observe how some of the things around us are arranged, as well as some of the changes in these arrangements. In some cases, moreover, we may find it possible not only to observe the changes going on around us, but also to influence them, a fact which raises fascinating issues more suitable for discussion in a different essay.
Moreover, unless we make the extraordinarily improbable assumption that our location in the universe is somehow uniquely “privileged,” it follows that observers located elsewhere in the universe will share these same sorts of primitive observations. In other words, they also will find that the things they observe are arranged in particular ways, at least some of which are subject to change. (Admittedly, the things they find around them conceivably might consist partly or solely of things unfamiliar to us such as dark matter or antimatter, for example, but this does not alter the point being made here.)
V. USING OUR WORDS TO TALK ABOUT TIME
I hope few would quarrel with the assertion that these sorts of primitive empirical observations far predate our invention of language. When language finally was invented at a relatively recent stage of human evolution, its first use undoubtedly was to promote the survival of its inventors. Later, our predecessors, seeking to describe and understand their environment, began using language to describe their observations regarding the changing configurations of the universe, things such as the cycles of the moon, for example. At some point, they inevitably sought to convey in words the closely related notions which we now think of and refer to as “a particular time” and as “the flow of time.”
Another useful way to think about particular times in this context is in terms of what often are referred to as “events.” The word event may refer to something as specific and brief as a batter hitting a home run in a World Series baseball game or to something as extended spatially and temporally as a World War. Events, of course, are always simply parts of larger configurations of the universe. Before the invention of writing, history was passed from generation to generation through a tradition of oral repetition in which descriptions of events important to the history of a family or clan or tribe certainly would have occupied a central role. Thus, it follows that our ancestors undoubtedly were talking about configurations of the universe (almost certainly without using this terminology) long before the invention of writing.
Our current knowledge of history derives from recorded descriptions of historical events and the actors who participated in them. These recorded descriptions of events represent relatively minuscule fragments of vastly broader, intrinsically unknowable, configurations of the universe. Should we wish our description of an event to be as inclusive as possible, it would have to include details such as the relative positions of innumerable far-flung galaxies and the precise relative positions of innumerable individual atoms, for example. Generally, however, such details are not central to what is, for us, the crux of these events. Consequently, we simply choose to ignore these broader contexts. In practice, we have found that events or particular times (i.e., configurations of the universe) may be described as carefully and precisely or as loosely as we choose and still retain some varying degree of practical utility.
Prior to the invention of calendars and clocks, which occurred relatively recently (barely the blink of an eye in evolutionary terms), our ideas about particular times had remained relatively vague and imprecise, hinging not upon the reading of a calendar or clock, but upon some obvious change in the configuration of the universe. Intervals between events were described in terms of units such as the numbers of “moons” or days between the events.
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. If I ask you to think about and describe how our world today differs from the world as it was in the 1st century BCE, for example, it almost certainly will lead you to conjure up some mental images of differences between these two particular times, i.e., between these two configurations of the universe. The precise nature of the differences conjured up in your mind in this case would depend on how carefully you have studied and memorized history; in other words, on how much information you can recall from your memory bank about recorded descriptions of the configuration of the universe which we refer to as the 1st century BCE.
Were I to ask you to think about and describe how our world today differs from the world as it was yesterday, however, it would not greatly tax your knowledge of ancient history. Rather, it would test your knowledge of current events. Nevertheless, it would leave little doubt that the configuration of the universe which we refer to as yesterday was significantly different from the configuration which we refer to as today or as now.
With the invention of calendars and clocks, our thinking, speaking, and writing about time began a relatively rapid and dramatic transformation. What previously had been rough descriptions of changing configurations of the universe now were being redefined to have ever narrower meanings. Henceforth, we could talk about our calendars and clocks “marking the passage of time,” for example, or “measuring the passage of time,” or, much more insidiously, in my opinion, we could talk about them “measuring time.” (I suspect that Lee Smolin might profitably begin seeking here for the scent of a trail leading to where and how the concept of time as used in physics may have gone awry.)
Suddenly, “time” had become a commodity which could be measured with precision, just as distance and mass could be measured. This, in turn, led, perhaps understandably, to the common perception (or perhaps misperception) that “time,” in and of itself, separate and distinct from the broader notion of evolving configurations of the universe from whence it sprang, was something ontologically real. Perhaps the rationale was that if we could talk about it and measure it, how could it not be real?
Ultimately, a unit of time -- the second -- assumed an honored place alongside the meter and the kilogram as a standard unit of measure, thereby solidifying and officially announcing time’s status as one of the fundamental building blocks of nature. The original definition of a second as the fraction 1/86,400 of a mean solar day retained at least a tenuous connection with the lineage relating it to evolving configurations of the universe. Even this connection was essentially lost, however, when the second subsequently was redefined in terms of oscillations of a cesium 133 atom.
VI. THE FLOW OF TIME
Please return now to my earlier question about how the particular time at which you are reading this sentence differs from the particular time five minutes prior to your having read it, or how it differs from the particular times one hour or one day or one year or one century prior to your having read it. Again, the only difference between these particular times, I maintain, lies in the arrangement of all the various bits and pieces of the universe, relative to one another, at each of these particular times.
Assuming one is willing, at least for the sake of argument, to grant this assertion, it then becomes reasonable to ask how the particular time which we refer to as one century ago, for example, became the particular time at which you are reading this sentence, i.e., the present. The way it happened is amazingly simple; the various bits and pieces which made up the universe one century ago subsequently have been rather dramatically rearranged, courtesy of the laws of physics.
The bits and pieces which existed a century ago certainly did not vanish. Quite the contrary; if someone had been so thoughtful as to put convenient little tags on all those small bits and pieces (say, on all the atoms, for example) which existed a century ago we would find that most of those very same small bits and pieces are still with us today. But they are arranged quite differently. The military uniform that a soldier was wearing one century ago, for example, might be tucked away in a trunk in an attic today, or it might reside in a museum somewhere, or perhaps it was burned, intentionally or otherwise, and the atoms of which it was made thus dispersed back into the universe.
The same is true, of course, regarding the particular time five minutes prior to your having read this sentence; in the latter case this may seem somewhat more obvious. The computer or other device you are using to read this sentence (along with the atoms of which it is made) did not suddenly vanish five minutes ago and then magically reappear just now; it has remained in more or less the same location relative to you that it had five minutes ago, but during this same interval your dog or cat may have walked across the room, a fire truck may have raced down the street past your house, and the Earth moved many miles in its orbit around the sun. In other words, the configuration of the universe has changed; it has evolved.
At some unknown point in history as our predecessors observed the ever-changing configurations of the universe, they began referring to these changing configurations as “the flow of time,” and it is easy to understand how this comparison between a flowing river and the ever-changing configurations of the universe might have arisen. It is absolutely crucial to recognize here, and to point out explicitly, however, that these changes in the configuration of the universe are not caused by, and are not in any way a consequence of, any “flow of time.” Rather, the changes we observe (as well as those we don’t observe) are the flow of time. If the configuration of the universe did not change, there would be no flow of time.
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.
To summarize, 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. If this is granted, then it should come as no surprise that there is a so-called “causal arrow of time.” In fact, there is no way that there possibly could not be a causal arrow of time, aside from a situation in which the universe was in a state of thermal equilibrium.
The terms “past” and “future” refer to configurations of the universe which we can visualize in our imaginations and about which we can speculate and hypothesize, but which have no objective reality for those of us who are living in the present. Our empirical observations lead us to conclude that the “past” consists of those configurations of the universe which once had an objective reality, i.e., which once actually existed. These past configurations subsequently have evolved, through physical displacements of the various bits and pieces relative to one another into the “present” configuration, some small portions of which we can perceive with our senses. And we infer that this configuration will evolve into yet others which we imagine as the “future.” In essence, the universe may be the ultimate example of “what you see is what you get.”
We can only engage in educated speculation about what sorts of things will or will not be included in future configurations of the universe. By understanding the laws of physics, we can predict or extrapolate, more or less accurately, the likely future configurations of at least some gross, observable features of the universe, up to a point, but we observe no empirical evidence of the objective reality of these predicted configurations. We find no ”fossilized remains” of the future as we do of the past, the reason being that the future, unlike the past, has never existed.
One will see that this way of thinking about the flow of time is significantly different from other concepts in which “events” are visualized as “flowing” from being in the future to being in the present and then finally to being forever in the past. In the view presented here “events” are synonymous with configurations of the universe. As the configuration of the universe evolves, in a manner governed by the laws of physics, the various configurations (arrangements) change. Events exist only so long as the configurations of the universe which define them exist.
VII. THE OPERATIONAL DEFINITION OF TIME
Because the operational definition of time (i.e., time is that which is measured by clocks) has proven to be so unquestionably successful I would be remiss if I did not discuss it further.
While not in any way intending to downplay or gainsay its impressive and unquestionable history of brilliant successes, I admit to being troubled by some aspects of the operational definition. To be clear, I do not believe that there is anything wrong with the operational definition, per se. It is, after all, a definition. This not withstanding, I have an uneasy sense that there is something about the operational definition which perhaps can best be described as a lack of “completeness.” Simply stating that time is that which is measured by clocks does not offer a great deal of insight into the underlying nature of reality. And yet the various theories which are based on the operational definition purport to do just that; i.e., they purport to reveal deep insights into the underlying nature of reality. How would that come about?
For example, theories based on the operational definition purport to reveal that the past, present, and future are all equally real and that what we perceive as the flow of time is illusory (the notion of a so-called "block time" or "block universe") and that time travel theoretically is possible. All three of these assertions are, according to the view presented here, incorrect.
I cannot escape an impression of the operational definition, together with the various theories based on that definition, as constituting a closed, internally consistent system which produces excellent mathematical results - - making possible our use of technological marvels such as the satellite-based Global Positioning System, for example - - but only so long as one remains wholly within that closed system. Is it possible, however, that some aspects of nature may not fall conveniently within that system? Could the longstanding lack of success in merging general relativity and quantum mechanics, for example, be symptomatic of such a possibility?
I also have been troubled by what appears to be a logical circularity in the operational definition; if time is that which is measured by clocks, it seems only fair to ask what constitutes a clock. The short answer, of course, is that a clock is a device which measures time. Physicists who are proponents of the operational definition go to great lengths to convince and reassure us that there is no troublesome circularity here. Clocks, they assure us, are physical devices constructed according to principles which allow them to undergo and count perfectly regular, cyclical motions of things such as pendulums or states of cesium atoms or photons bouncing back and forth between two mirrors, for example. Typically not adequately explained, however, is how one would know whether such oscillations were “perfectly regular” or not without using another clock to measure them, etc., ad infinitum.
Certainly among the most curious and puzzling implications of the operational definition is the logical consequence (via Einstein’s special relativity, which in turn is based on the operational definition) that there can be no such thing as a real, objective flow of time, and that what we perceive as the flow of time is illusory. As a substitute for the notion of the flow of time, it becomes logically necessary under this scenario to accept the concept of block time in which all times, past, present, and future are equally real. Even Einstein himself was troubled by this logical progeny.
Among the clearest explanations of the operational definition of time and its implications can be found in Brian Greene’s The Elegant Universe  and his later work The Fabric of the Cosmos , which both are recommended reading for anyone interested in learning more about what may be thought of as the orthodox view of the operational definition and some of its implications.
The crux of how the operational definition supposedly leads inexorably to a belief in block time may be found in The Fabric of the Cosmos in a chapter titled, “The Frozen River: Does Time Flow?” Greene describes there what he refers to as a “now-list,” consisting of a mental freeze-frame image of the entire universe right now. He then points out, correctly, that the knowledge of the universe available to any particular observer is severely circumscribed by the speed of light. Greene then goes on to write,
“ . . . according to Newton’s absolute space and absolute time, everyone’s freeze-frame picture of the universe at a given moment contains exactly the same events; everyone’s now is the same now, and so everyone’s now-list for a given moment is identical. If someone or something is on your now-list for a given moment, then it is necessarily also on my now-list for that moment. Most people’s intuition is still bound up with this way of thinking, but special relativity tells a very different story. . . . Observers moving relative to each other have different conceptions of what exists at a given moment, and hence they have different conceptions of reality.
. . . .
So: if you buy the notion that reality consists of the things in your freeze-frame mental image right now, and if you agree that your now is no more valid than the now of someone located far away in space who can move freely, then reality encompasses all of the events in spacetime. . . . Just as we envision all of space as really being out there, as really existing, we should also envision all of time as really being out there, as really existing, too.” [Greene’s italics] 
But I do not buy this notion. Recognizing that my knowledge about the configuration of the universe is severely circumscribed by the sensory data upon which I rely to construct such knowledge, I am necessarily cautious in making assumptions about what may or may not be on the now-list of someone in another part of the universe, especially someone located far away. Even observers who are local to one another and who are not moving relative to one another will have slightly different conceptions of what exists at a given moment.
I do, however, buy the notion that observers who are local to one another and who are not moving at speeds approaching the speed of light relative to one another would be able to reach some reasonably good agreement about the configuration of the portion of the universe accessible from their location. Absent this, science would not be possible.
Greene's proposed mental freeze-frame image of the entire universe -- were it possible -- would be identical to what I have called a particular configuration of the universe. Such an image, unfortunately, would be available only to some hypothetical godlike being not subject to the limitations imposed on human beings by the nature of sensory data available to them. In reality, our perceptions represent little more than a "best approximation" of what objectively exists in whatever portion of the universe we are able to observe. Given these real-world limitations, I find myself unable to make the leap of logic which -- if I understand him correctly -- Greene (along with other proponents of block time) apparently has proposed: namely, that because different observers will have different best approximations of what objectively exists (with no one of these best approximations being any more intrinsically valid than any other), then a multitude of objective realities must coexist. The universe has one, and only one, real history, albeit one which may be perceived differently by different observers.
When theories based on the operational definition lead to a claim that our primitive empirical observations regarding the flow of time are illusory, and when they lead to a claim that all times -- past, present, and future -- are equally real, we should -- at a minimum -- question whether the operational definition, along with the theories based on it, are perhaps being extended beyond their rightful range of applicability. If so, we would be at risk of blurring an important distinction between what is merely a mathematical description of reality and the underlying objective reality itself.
To sum up, the operational definition of time and its offspring, special relativity, seem ill-suited to explain our primitive empirical observations regarding evolving configurations of the universe which we refer to as the flow of time. As Julian Barbour wrote in The End of Time, “Relativity is not about an abstract concept of time at all: it is about physical devices called clocks. Once we grasp that, many difficulties fall away” . I might add to this the suggestion that the only “clock” which really matters is the universe itself.
VIII. NOT MERELY A DISTINCTION WITHOUT A DIFFERENCE
Importantly, it is not difficult to cite examples of how the concept of time proposed in this essay leads to clear, unambiguous conclusions which are dramatically and starkly different from conclusions which generally are believed to flow directly from the operational definition of time. These go much farther and much deeper than being mere distinctions without a difference. Moreover, at least some of the differences concern issues which ultimately are falsifiable, and thus well within the domain of science.
For one thing, the concept of time proposed here, unlike the operational definition, absolutely rules out the possibility of time travel. The reasons for this are spelled out in detail in my essay, On the Impossibility of Time Travel, which is available on the Internet . Clearly, time travel either is or is not possible; we cannot forever continue to have it both ways. I believe that the reason this topic has remained ambiguous and uncertain for so long is that too many of those who have spoken and written about time travel have not been sufficiently careful in their use of words. I have attempted to correct this ambiguity and lack of clarity in my essay on the topic referred to above.
Likewise, the concept espoused here is fundamentally incompatible with the concept of block time or a block universe. All times, past, present, and future, definitely do not exist with equal reality in the proposed concept. In fact, I believe the concept directly answers Greene's conjecture that someone ". . . will one day devise a new way of looking at time and reveal a bona fide physical foundation for a time that flows" . This concept does exactly that, in my opinion.
On the other hand, the concept of time proposed here is consistent with another falsifiable conclusion supported by the operational definition, namely, the equivalence of mass and energy. An argument supporting this contention will be found in my essay, Time: Illusion and Reality .
IX. GOING FORWARD
Having failed to come up with a suitably catchy name for the concept of time proposed in this essay, I am reluctant to glorify it by using the term “paradigm” to describe it. In the sense that the concept offers a potentially useful framework for thinking about the nature of time and the nature of reality, however, perhaps the term fits.
I harbor no illusions that even a general acceptance of the concept proposed here would magically solve all the many outstanding questions about the nature of time; in fact, it almost certainly would be accompanied by an entirely new set of questions. Nevertheless, I believe it would be at least a small step in the right direction. Adopting a paradigm which more closely reflects the underlying nature of reality, as I believe this does, can only have a positive influence on the direction of science. As Kuhn so aptly stated, “paradigms provide scientists not only with a map but also with some of the directions essential for map-making" .
The proposed concept, if accepted, should silence fruitless chatter about whether time exists or not. Clearly, whether time exists or not depends entirely on how one defines time. If particular times are defined as being identically equivalent to particular real but intrinsically unknowable configurations of an evolving universe, and if the flow of time is defined to be the evolution of the physical universe, then yes, time does exist. If it is defined to be something separate and independent from these things, then no, it does not exist. As Barbour wrote, “. . . the important thing is to get away from the idea that time is something. Time does not exist. All that exists are things that change. What we call time is - - in classical physics at least - - simply a complex of rules that govern the change.” [Barbour’s italics] 
It will not have escaped the attention of readers closely familiar with this topic that the word “simultaneity” has not appeared in the current essay until this sentence. Simultaneity clearly is a topic which has loomed large in writings on the philosophy and science of time. I believe that the concept of time proposed in this essay has strong implications for the notion of simultaneity, but I beg forgiveness for choosing not to address that topic in this essay, which already has grown far too long and unwieldy.
While doing little to assuage suspicions held by some that we sentient beings are, in essence, mere flotsam adrift in an ever-changing, ever-evolving universe, the concept of time proposed here might bring us a step closer to a better understanding of the nature of reality. Such insight, in turn, might improve our chances of survival, and, ultimately, perhaps even our sense of being at home in the universe.
One of the most intriguing aspects of the universe in which we find ourselves is, in my opinion, the notion that each of us can, by our own actions, have some influence, albeit limited, on future configurations of the universe. It would appear to be in our own enlightened self-interest, therefore, to use our individual and collective powers, limited though they may be, to influence the evolution of the universe in ways that will make subsequent configurations as habitable, pleasant, and rewarding as possible.
 Brian Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, Alfred A. Knopf/Random House, New York/Toronto, 2004.
 Jürgen Neffe, Einstein: A Biography, Farrar, Straus and Giroux, New York, 2005, Translation by Shelley Frisch, 2007.
 Lee Smolin, The Trouble With Physics, Houghton Mifflin Co., New York, 2006.
 J. C. N. Smith, Time: Illusion and Reality: An Unconventional but Constructive Look at the Fundamental Nature of Time, http://sites.google.com/site/smithjcn/time.
 Thomas S. Kuhn, The Structure of Scientific Revolutions, The University of Chicago Press, Chicago, 1962.
 John Archibald Wheeler, Quoted from an interview by Science News Magazine Editor in Chief Tom Siegfried, Science News (web edition), May 12th, 2008.
 Barry Dainton, Time and Space, Second Edition, McGill-Queen's University Press, Canada, 2010.
 Julian Barbour, The End of Time, Oxford University Press, New York and Weidenfeld & Nicolson, London, 1999.
 Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Vintage Books/Random House, New York and Toronto, 1999.
 J. C. N. Smith, On the Impossibility of Time Travel, http://www.fqxi.org/data/essay-contest-files/Smith_IOTT6.cwk.pdf.