Time is what clocks measure. We use our concept of time to place events in sequence one after the other, to compare how long an event lasts, and to tell when an event occurs. Those are three key features of time. Yet despite 2,500 years of investigating time, many issues about it are unresolved. Here is a short list in no particular order of the most important ones: •What time actually is; •Whether time exists when nothing is changing; •What kinds of time travel are possible; •Why time has an arrow; •Whether the future and past are as real as the present; •How to analyze the metaphor of time’s flow; •Whether future time will be infinite; •Whether there was time before the Big Bang event; •Whether tensed or tenseless concepts are semantically basic; •What the proper formalism or logic is for capturing the special role that time plays in reasoning; •What neural mechanisms account for our experience of time; •Why there isn’t more than one dimension of time; and •Whether there is a timeless nature beyond spacetime.

Some of these issues will be resolved by scientific advances alone, but others require philosophical analysis. For example, we expect that it will take a discovery of some new scientific principles to explain why time has only one dimension, but we expect that answering the question of whether the future is real is a matter for philosophical analysis.

Consider this one issue upon which philosophers are deeply divided: What sort of ontological differences are there among the present, past and future? There are three competing theories. Presentists argue that necessarily only present objects and present experiences are real, and we conscious beings recognize this in the special “vividness” of our present experience. The dinosaurs have slipped out of reality. However, according to the growing-universe or growing-block theory, the past and present are both real, but the future is not real because the future is indeterminate or merely potential. Dinosaurs are real, but our death is not. The third and more popular theory is that there are no significant ontological differences among present, past, and future because the differences are merely subjective. This view is called “the block universe theory” or “eternalism.”

That controversy raises the issue of tenseless versus tensed theories of time. The block universe theory implies a tenseless theory. The earliest version of this theory implied that tensed terminology can be replaced adequately with tenseless terminology. For example, the future-tensed sentence, “The Lakers will win the basketball game” might be analyzed as, “The Lakers do win at time t, and time t happens after the time of this utterance.” Notice that the future tense has been removed, and the new verb phrases “do win” and “happens after” are tenseless logically, although they are grammatically in the present tense. (Similarly, the present-tense verb “is” in “seven plus five is twelve” isn’t only about the present.) Advocates of a tensed theory object and say that tenseless terminology is not semantically basic but should be analyzed in tensed terms, and that tensed facts are needed to make tensed statements be true. For example, a tensed theory might imply that no adequate account of the present tensed fact that it is now midnight can be given without irreducible tensed properties such as presentness or now-ness. So, the philosophical debate is over whether tensed concepts have semantical priority over untensed concepts, and whether tensed facts have ontological priority over untensed facts.

Table of Contents

  1. What Should a Philosophical Theory of Time Do?
  2. How Is Time Related to Mind?
  3. What Is Time?
    1. The Variety of Answers
    2. Time vs. “Time”
    3. Defining Time Order with Causal Order
    4. Linear and Circular Time
    5. The Extent of Past Time
    6. Does Time Emerge from Something More Basic?
  4. What Does Science Require of Time?
  5. What Kinds of Time Travel Are Possible?
  6. Does Time Require Change? (Relational vs. Substantival Theories)
  7. Does Time Flow?
  8. What Gives Time Its Direction or Arrow?
    1. What Needs To Be Explained?
    2. Explanations or Theories of the Arrow
    3. Multiple Arrows
    4. Reversing the Arrow
  9. Is Only the Present Real?
    1. Presentism, the Growing Past, and the Block Universe
    2. Enduring and Perduring Objects
    3. Truth Values and Free Will
  10. Are There Essentially-Tensed Facts?
  11. What is Temporal Logic?
  12. Supplements
    1. Frequently Asked Questions
    2. What Science Requires of Time
    3. Special Relativity: Proper Times, Coordinate Systems, and Lorentz Transformations (by Andrew Holster)
  13. References and Further Reading

1. What Should a Philosophical Theory of Time Do?

Should it define the word “time”? Yes, and as a working definition we can say time is a sequence of moments in a linear order. However, it is improper to demand that we give a very precise and detailed definition of the word as a prelude to saying anything more about time, in large part because definitions often need to be changed when more is learned. What we really want is to build a comprehensive, philosophical theory of time that helps us understand time by solving problems about time. We do not want to start building this theory by adopting a prior, unrevisable definition of time that might prejudice the theory-building project from the beginning.

Although there are theories of how to solve this or that specific problem about time, it is always better to knit together solutions to several problems. Ideally, the goal is to produce a theory of time that will solve in a systematic way the constellation of problems involving time. What are those problems?

One is to clarify the relationship between time and the mind. For example, does time exist for beings that have no minds? It is easy to confuse time itself with the perception of time.

Another problem is to decide which of our intuitive beliefs about time should be retained when they conflict with other beliefs. Some of these intuitions may reflect deep insights into the nature of time, and others may be faulty ideas inherited from our predecessors. It is not obvious which is which. For one example, if we have the intuition that time flows, but a scientific theory implies otherwise, then is this sufficient reason to reject the scientific theory?

A third problem for a philosophical theory of time is to clarify what physical science presupposes and implies about time. A later section of this article examines this topic. Most all philosophers of time claim that philosophical theories should be consistent with physical science, or, if not, then they must accept the heavy burden of proof to justify the inconsistency.

A philosophical theory of time should describe the relationship between instants and events. Does the instant that we label as “11:01 A.M.” for a certain date exist independently of the events that occur then? In other words, can time exist if no event is happening? This question or problem raises the thorny metaphysical issue of relational vs. substantival  theories of time.

A theory of time should address the question of explaining time’s apparent direction. In space, you can go your direction and I can go mine, but in time we all go the same direction, so to speak. Why is that? If we were to view a movie of brown coffee separating into black coffee—with cream leaving it and flying up into the pitcher—we in the audience could immediately tell that the actual events did not occur in this order. We recognize this arrow of time because we know about the one-directional processes in nature. However, this unidirectionality or arrow becomes less and less apparent to us viewers as the movie subject gets smaller and smaller and the time interval gets shorter and shorter until finally we are viewing processes that could just as easily go the other way, at which point the arrow of time has disappeared. Philosophers disagree about how to explain the existence of the arrow.

Another philosophical problem about time concerns the two questions, “What is the present, and why does it move into the past?” If we know what the present is, then we ought to be able to answer this question: “How long does the present last?” And regarding the second question about the “movement” of the present into the past, many philosophers are suspicious of this notion of the flow of time, the march of time. They doubt whether it is a property of time as opposed to being some feature of human perception, although they do not doubt that time has a direction or arrow. Yet other philosophers are adamant that the flow is quite real objectively.

Are there ontological differences among the past, present, and future? Some philosophers doubt whether the future and past are as real as the present, the feature that is referred to by the word “now.” A famous philosophical argument says that, if the future were real, then it would be fixed now, and we would not have the freedom to affect that future. Since we do have that freedom, the future can not be real. Some philosophers consider this to be a clever, but faulty argument.

For a last example of a philosophical issue regarding time, is time a fundamental feature of nature, or does it emerge from more basic features–in analogy to the way the smoothness of water flow emerges from the complicated behavior of the underlying molecules?

A full theory of time should address this constellation of philosophical issues about time. Narrower theories of time will focus on resolving one or more members of this constellation, but the long-range goal is to knit together these theories into a full, systematic, and detailed theory of time.

Philosophers of time tend to divide into two broad camps on the philosophical issues, although many philosophers do not fit into these pigeonholes. Members of the first camp say that the now is objectively real and so is time’s flow, McTaggart’s A-theory is the right way to view time, ontologically we should accept either presentism or the growing-past theory, predictions are not true or false at the time they are uttered, tenses are semantically basic, and the fundamental entities are 3-dimensional objects. Members of the second camp say that the now is subjective and so is time’s flow, McTaggart’s B-theory is the right way to view time, ontologically we should accept eternalism or the block universe theory, predictions are true or false at the time they are uttered, tenses are not semantically basic, and the fundamental entities are 4-dimensional events. This article is intended to provide an introduction to this controversy between the two camps.

2. How Is Time Related to Mind?

Physical time is public time, the time that clocks are designed to measure. Psychological time or phenomenological time is private time. It is perhaps best understood as awareness of physical time. Psychological time passes relatively swiftly for us while we are enjoying an activity, but it slows dramatically if we are waiting anxiously for the water to boil on the stove. The slowness is probably due to focusing our attention on short intervals of physical time. Meanwhile, the clock by the stove is measuring physical time and is not affected by anybody’s awareness. Some philosophers claim that psychological time is completely transcended in the mental state called nirvana because psychological time slows to a complete stop.

When a physicist defines speed to be the rate of change of position with respect to time, the term “time” refers to physical time. Physical time is more basic for helping us understand our shared experiences in the world, and so it is more useful than psychological time for doing science. But psychological time is vitally important for understanding many human thought processes.

Within the field of cognitive science, one wants to know what are the neural mechanisms that account not only for our experience of time’s flow, but also for our ability to place events into the proper time order. See (Damasio, 2006) for further discussion of the progress in this area of cognitive science. The most surprising experimental result about psychological time is Benjamin Libet’s experiments in the 1970s that show, or so it is claimed, that the brain events involved in initiating our free choices occur about a third of a second before we are aware of our choice. Before Libet’s work, it was universally agreed that a person is aware of deciding to act freely, then later the body initiates the action.

Linguists have investigated how our growing up speaking one natural language rather than another can affect our mental representation of psychological time.

Psychologists are interested in whether we can speed up our minds relative to physical time. If so, we might become mentally more productive, get more high quality decision making done per fixed amount of physical time, learn more per minute. Several avenues have been explored: using drugs such as cocaine and amphetamines, undergoing extreme experiences such as jumping backwards off a tall tower with bungee cords attached to the legs, and trying different forms of meditation. So far, none of these avenues have led to success productivity-wise.

Any organism’s sense of time is subjective, but is the time that is sensed also subjective, a mind-dependent phenomenon? Without minds in the world, nothing in the world would be surprising or beautiful or interesting. Can we add that nothing would be in time? If judgments of time were subjective in the way judgments of being interesting vs. not-interesting are subjective, then it would be miraculous that everyone can so easily agree on the ordering of public events in time. For example, first, Einstein was born, then he went to school, then he died. Everybody agrees that it happened in this order: birth, school, death. No other order. The agreement on time order for so many events is part of the reason that most philosophers and scientists believe physical time is an objective phenomenon that is not dependent on being consciously experienced. Another part of the reason time is believed to be objective is that our universe has a large number of different processes that bear consistent time relations, or frequency of occurrence relations, to each other. For example, the frequency of rotation of the Earth around its axis is a constant multiple of the frequency of oscillation of a fixed-length pendulum, which in turn is a constant multiple of the half life of a specific radioactive uranium isotope; the relationship does not change as time goes by (at least not much and not for a long time and when there is deviation we know how to predict it and compensate for it). The existence of these sorts of relationships makes our system of physical laws much simpler than it otherwise would be, and it makes us more confident that there is something objective we are referring to with the time-variable in those laws. The stability of these relationships over a long time also makes it easy to create clocks. Time can be measured easily because we have access to long-term simple harmonic oscillators that have a regular period or “regular ticking.” This regularity shows up in completely different stable systems when they are disturbed: a ball swinging from a string (a pendulum), a ball bouncing up and down from a coiled spring, a planet orbiting the Sun, organ pipes, electric circuits, and atoms in a crystal lattice. Many of these systems make good clocks.

Aristotle raised this issue of the mind-dependence of time when he said, “Whether, if soul (mind) did not exist, time would exist or not, is a question that may fairly be asked; for if there cannot be someone to count there cannot be anything that can be counted…” [Physics, chapter 14]. He does not answer his own question because, he says rather profoundly, it depends on whether time is the conscious numbering of movement or instead is just the capability of movements being numbered were consciousness to exist.

St. Augustine, adopting a subjective view of time, said time is nothing in reality but exists only in the mind’s apprehension of that reality. In the 11th century, the Persian philosopher Avicenna doubted the existence of physical time, arguing that time exists only in the mind due to memory and expectation. The 13th century philosophers Henry of Ghent and Giles of Rome said time exists in reality as a mind-independent continuum, but is distinguished into earlier and later parts only by the mind. In the 13th century, Duns Scotus clearly recognized both physical and psychological time.

At the end of the 18th century, Kant suggested a subtle relationship between time and mind–that our mind actually structures our perceptions so that we can know a priori that time is like a mathematical line. Time is, on this theory, a form of conscious experience, and our sense of time is a necessary condition of our experience or sensation. In the 19th century, Ernst Mach claimed instead that our sense of time is a simple sensation, not an a priori form of sensation. This controversy took another turn when other philosophers argued that both Kant and Mach were incorrect because our sense of time is an intellectual construction (see Whitrow, p. 64).

In the 20th century, the philosopher of science Bas van Fraassen described physical time by saying, “There would be no time were there no beings capable of reason” just as “there would be no food were there no organisms, and no teacups if there were no tea drinkers,” and no cultural objects without a culture.

The controversy in metaphysics between idealism and realism is that, for the idealist, nothing exists independently of the mind. If this controversy is settled in favor of idealism, then time, too, would have that subjective feature–physical time as well as psychological time.

It has been suggested by some philosophers that Einstein’s theory of relativity, when confirmed, showed us that time depends on the observer, and thus that time is subjective, or dependent on the mind. This error is probably caused by Einstein’s use of the term “observer.” Einstein’s theory does imply that the duration of an event is not observer-independent but depends on the observer’s frame of reference or coordinate system. But what Einstein means by “observer’s frame of reference” is merely a perspective or coordinate framework from which measurements could be made. The “observer” does not have to be a conscious being or have a mind. So, Einstein is not making a point about mind-dependence.

For more on the consciousness of time and related issues, see the article “Phenomenology and Time-Consciousness.”

3. What Is Time?

We use our concept of time to place events in sequence one after the other, to compare how long an event lasts, and to tell when an event occurs. These are the three key features of time. But those features do not tell us what time itself is.

a. The Variety of Answers

Among philosophers of physics, the most popular short answer to the question “What is physical time?” is that it is not a substance or object but rather a special system of relations among instantaneous events. This working definition is offered by Adolf Grünbaum who applies the contemporary mathematical theory of continuity to physical processes, and he says time is a linear continuum of instants and is a distinguished one-dimensional sub-space of four-dimensional spacetime.

How do we tell whether this is the correct answer to our question? To be convinced, we need to be told what the relevant terms mean, such as “special system of relations.” In addition, we need to be presented with a theory of time implying that time is this system of relations; and we need to be shown how that theory adequately addresses the many features that are required for a successful theory of time. Finally, we need to compare this theory to its alternatives. This article will not carry out these tasks.

A different, but popular answer to the question “What is time?” is that time is the form of becoming. To assess this answer, which is from Alfred North Whitehead, we need to be told what the term “form of becoming” means; we need to be presented with a detailed theory of time implying that time is the form of becoming; and we need to investigate how it addresses those many features required for a successful theory of time.

If physical time and psychological time are two different kinds of time, then two answers are required to the question “What is time?” and some commentary is required regarding their relationships, such as whether one is more fundamental. Many philosophers of science argue that physical time is more fundamental even though psychological time is discovered first by each of us as we grow out of our childhood, and even though psychological time was discovered first as we human beings evolved from our animal ancestors. The remainder of this article focuses more on physical time than psychological time.

Another answer to our question, “What is time?” is that time is whatever the time variable t is denoting in the best-confirmed and most fundamental theories of current science. “Time” is given an implicit definition this way. Nearly all philosophers would agree that we do learn much about physical time by looking at the behavior of the time variable in these theories; but they complain that the full nature of physical time can be revealed only with a philosophical theory of time that addresses the many philosophical issues that scientists do not concern themselves with.

Michael Dummett’s constructive model of time implies that time is a composition of intervals rather than of durationless instants. The model is constructive in the sense that it implies there do not exist any times which are not detectable in principle by a physical process.

An additional answer to our question is that time is a substance, not a relationship among events. It is a distinguished one-dimensional sub-space of spacetime, and spacetime is a substance. This substantivalist answer is explored in a later section.

Bothered by the contradictions they claimed to find in our concept of time, Zeno, Plato, Spinoza, Hegel, and McTaggart answer the question, “What is time?” by replying that it is nothing because it does not exist. In a similar vein, the early 20th century English philosopher F. H. Bradley argues, “Time, like space, has most evidently proved not to be real, but a contradictory appearance….The problem of change defies solution.” In the mid-twentieth century, Gödel argued for the unreality of time because Einstein’s equations allow for events to precede themselves.  In the twenty-first century physicists hoping to reconcile general relativity with quantum mechanics are suggesting that either time does not exist or else it is not fundamental in nature; see Callender (2010). However, most philosophers agree that time does exist. They just can not agree on what it is.

Let’s briefly explore other answers that have been given throughout history to our question, “What is time?” Aristotle claimed that “time is the measure of change” [Physics, chapter 12], but he emphasized “that time is not change [itself]” because a change “may be faster or slower, but not time…” [Physics, chapter 10]. For example, a specific change such as the descent of a leaf can be faster or slower, but time itself can not be faster or slower. In developing his views about time, Aristotle advocated what is now referred to as the relational theory when he said, “there is no time apart from change….” [Physics, chapter 11]. In addition, Aristotle said time is not discrete or atomistic but “is continuous…. In respect of size there is no minimum; for every line is divided ad infinitum. Hence it is so with time” [Physics, chapter 11].

René Descartes had a very different answer to “What is time?” He argued that a material body has the property of spatial extension but no inherent capacity for temporal endurance, and that God by his continual action sustains (or re-creates) the body at each successive instant. Time is a kind of sustenance or re-creation. ["Third Meditation" in Meditations on First Philosophy]

In the 17th century, the English physicist Isaac Barrow rejected Aristotle’s linkage between time and change. Barrow said time is something which exists independently of motion or change and which existed even before God created the matter in the universe. Barrow’s student, Isaac Newton, agreed with this substantival theory of time. Newton argued very specifically that time and space are an infinitely large container for all events, and that the container exists with or without the events. He added that space and time are not material substances, but are like substances in not being dependent on anything except God.

Gottfried Leibniz objected. He argued that time is not an entity existing independently of actual events. He insisted that Newton had underemphasized the fact that time necessarily involves an ordering of any pair of non-simultaneous events. This is why time “needs” events, so to speak. Leibniz added that this overall order is time. He accepts a relational theory of time and rejects a substantival theory.

In the 18th century, Immanuel Kant said time and space are forms that the mind projects upon the external things-in-themselves. He spoke of our mind structuring our perceptions so that space always has a Euclidean geometry, and time has the structure of the mathematical line. Kant’s idea that time is a form of apprehending phenomena is probably best taken as suggesting that we have no direct perception of time but only the ability to experience things and events in time. Some historians distinguish perceptual space from physical space and say that Kant was right about perceptual space. It is difficult, though, to get a clear concept of perceptual space. If physical space and perceptual space are the same thing, then Kant is claiming we know a priori that physical space is Euclidean. With the discovery of non-Euclidean geometries in the 1820s, and with increased doubt about the reliability of Kant’s method of transcendental proof, the view that truths about space and time are a priori truths began to lose favor.

The above discussion does not exhaust all the claims about what time is. And there is no sharp line between giving a definition of time and remarking on some important characteristic of time.

b. Time vs. “Time”

Whatever time is, it is not “time.” One has four letters; the other does not. Nevertheless, it might help us understand time if we improved our understanding of the sense of the word “time.” Should the proper answer to the question “What is time?” produce a definition of the word as a means of capturing its sense? Definitely not–if the definition must be some analysis that provides a simple paraphrase in all its occurrences. There are just too many varied occurrences of the word: time out, behind the times, in the nick of time, and so forth.

But how about narrowing the goal to a definition of the word “time” in its main sense, the sense that most interests philosophers and physicists? That is, explore the usage of the word “time” in its principal sense as a means of learning what time is. Well, this project would require some consideration of the grammar of the word “time.” Most philosophers today would agree with A. N. Prior who remarked that, “there are genuine metaphysical problems, but I think you have to talk about grammar at least a little bit in order to solve most of them.” However, do we learn enough about what time is when we learn about the grammatical intricacies of the word? John Austin made this point in “A Plea for Excuses,” when he said, if we are using the analytic method, the method of analysis of language, in order to sharpen our perception of the phenomena, then “it is plainly preferable to investigate a field where ordinary language is rich and subtle, as it is in the pressingly practical matter of Excuses, but certainly is not in the matter, say, of Time.” Ordinary-language philosophers have studied time talk, what Wittgenstein called the “language game” of discourse about time. Wittgenstein’s expectation is that by drawing attention to ordinary ways of speaking we will be able to dissolve rather than answer our philosophical questions. But most philosophers of time are unsatisfied with this approach; they want the questions answered, not dissolved, although they are happy to have help from the ordinary language philosopher in clearing up misconceptions that may be produced by the way we use the word in our ordinary, non-technical discourse.

c. Defining Time Order with Causal Order

In 1924, Hans Reichenbach defined time order in terms of possible cause. Event A happens before event B if A could have caused B but B could not have caused A. This was the first causal theory of time, although Leibniz had said, “If of two elements which are not simultaneous one comprehends the cause of the other, then the former is considered as preceding, the latter as succeeding.” The usefulness of the causal theory depends on a clarification of the notorious notions of causality and possibility without producing a circular explanation that presupposes an understanding of time order. Reichenbach’s idea was that causal order can be explained in terms of the “fork asymmetry.” The asymmetry is due to the fact that outgoing processes from a common center tend to be correlated with one another, but incoming processes to a common center are uncorrelated. [Do you remember ever tossing a rock into a still pond? There’s a correlation among all sorts of later events such as the rock’s disappearing under the water, the water surface getting wavy, your hearing a splash sound, the water surging slightly up the bank at the edge of the pond, and even of the pond being warmer. Imagine what the initial conditions at the edge and bottom of the pond must be like to produce correlated, incoming, concentric water waves so that as they reach the center the rock flies out of the water, leaving the water surface smooth, and sound waves rush out of your ear and converge on the surface where the splash is not occurring, and the pond is left cooler.] Some philosophers argue that temporal asymmetry, but not temporal priority, can be analyzed in terms of causation. Put more simply, event A’s not occurring simultaneously with B can be analyzed in terms of cause and possible cause, but what can’t be analyzed in this manner is A’s occurring first. Even if Reichenbach were correct that temporal priority can be analyzed in terms of causation, the question remains whether time itself can be analyzed in those terms.

The usefulness of the causal theory also depends on a refutation of David Hume’s view that causation is simply a matter of constant conjunction [that is, event A's causing event B is simply B's always occurring if A does]. For Hume, there is nothing metaphysically deep about causes preceding their effects; it is just a matter of convention that we use the terms “cause” and “effect” to distinguish the earlier and later members of a pair of events which are related by constant conjunction.

d. Linear and Circular Time

If you travel to your past and then return to the place and moment of your leaving, your personal time (that is, proper time) is circular but your non-time-traveling twin’s personal time is linear. If your personal time were circular, you could be assured that either you’d never die or that after your death you would be reborn. With circular time, the future becomes the past. If your time is like this, then the question arises as to whether there would be an endless number of reoccurrences of a state of the world, or whether, accepting Leibniz’s Principle of the Identity of Indiscernibles, each supposedly repeating state of the world would occur just once because each state would not be discernible from the repeated state.

During history (and long before Einstein made a distinction between proper time and coordinates time), a variety of answers were given to the question of whether time is like a line or, instead, like a circle. The concept of linear time first appeared in the writings of the Hebrews and the Zoroastrian Iranians. The Roman writer Seneca also advocated linear time. Plato and most other Greeks and Romans believed time to be motion and believed cosmic motion was cyclical, but this was not envisioned as requiring any detailed endless repetition such as the multiple rebirths of Socrates. However, the Pythagoreans and some Stoic philosophers did adopt this drastic position. The idea was picked up again by Nietzsche in 1882 and Poincaré in 1890. Scholars do not agree on whether Nietzsche meant his idea of circular time to be taken literally or merely for a moral lesson about how you should live your life if you knew that you’d live it over and over, but Poincaré did intend his to be taken literally.

Islamic and Christian theologians adopted the ancient idea that time is linear plus the Jewish-Zoroastrian idea that the universe was created at a definite moment in the past. Augustine emphasized that human experience is a one-way journey from Genesis to Judgment, regardless of any recurring patterns or cycles in nature. In the Medieval period, Thomas Aquinas agreed. Nevertheless, it was not until 1602 that the concept of linear time was more clearly formulated–by the English philosopher Francis Bacon. In 1687, Newton advocated linear time when he represented time mathematically by using a continuous straight line. The concept of linear time was promoted by Barrow, Leibniz, Locke and Kant. In 19th century Europe, the idea of linear time became dominant in both science and philosophy. However, in the twentieth century, Gödel and others discovered solutions to the equations of Einstein’s general theory of relativity that allowed closed loops of proper time. These causal loops or closed curves in spacetime allow you to go forward continuously in time until you arrive back into your past. You will become your younger self in the future. As far as we can tell today, our universe does not exemplify any of these solutions to Einstein’s equations.

e. The Extent of Past Time

In ancient Greece, Aristotle claimed that time had an infinite past because, for any time, we always imagine an earlier time. The Greeks believed time existed before the Unmoved Mover intervened to create order from the previously existing chaos. In Medieval times, Aquinas objected to the ancient Greek view, saying past time is finite and that our imagination can’t always be trusted to tell us how things are. Instead, the past is finite because time began with God’s creation of Earth a finite time ago. In the late 17th century, Newton argued that time is infinite in the past and future. The classical Big Bang theory of the 20th century implies the past is finite, having begun only 13.7 billion years ago. Some newer, and more speculative, versions of the Big Bang theory allow time to exist before the Big Bang, possibly infinitely earlier.

f. Does Time Emerge from Something More Basic?

Is time ontologically basic, or does it depend on something even more basic? The question is asking whether there is nature beyond spacetime. We might rephrase this question by asking whether facts about time supervene on more basic facts. Facts about sound supervene on, or are a product of, facts about changes in the molecules of the air, so molecular change is more basic than sound. Minkowski argued in 1908 that we should believe spacetime is more basic than time, but is spacetime itself basic? Some physicists argue that both space and time are the product of some more basic micro-substrate, although there is no agreed-upon theory of what the substrate is. Other physicists say space is not basic, but time is. In 2004, after winning the Nobel Prize in physics, David Gross expressed this viewpoint:

Everyone in string theory is convinced…that spacetime is doomed. But we don’t know what it’s replaced by. We have an enormous amount of evidence that space is doomed. We even have examples, mathematically well-defined examples, where space is an emergent concept…. But in my opinion the tough problem that has not yet been faced up to at all is, “How do we imagine a dynamical theory of physics in which time is emergent?” …All the examples we have do not have an emergent time. They have emergent space but not time. It is very hard for me to imagine a formulation of physics without time as a primary concept because physics is typically thought of as predicting the future given the past. We have unitary time evolution. How could we have a theory of physics where we start with something in which time is never mentioned?

The discussion in this section about whether time is ontologically basic has no implications for whether the word “time” is semantically basic or whether the idea of time is basic to concept formation.

4. What Does Science Require of Time?

Science currently requires almost all the basic laws of science to be time symmetric. That means the laws can not change from one day to another. The three fundamental theories of physics, namely relativity, quantum mechanics and the Big Bang theory, all imply that any duration is a continuum very much like a segment of the real number line. So, time is not atomistic or discrete. Spacetime is more fundamental than either space or time alone, although time is not space because time is a distinguished, linear subspace of four-dimensional spacetime. Unlike in Newton’s physics and the physics of special relativity, spacetime is not a passive container for events; it is dynamic in the sense that changes in matter-energy can change the curvature of spacetime itself. Relativity implies that the duration of an event depends on the reference frame used in measuring the duration; and so does the order in which two events occur, although all correct observers must agree on the time order of two events that could be causally related. Specifying that an event lasted three minutes without giving even an implicit indication of the reference frame is like asking someone to stand over there and not giving any indication of where “there” is. Relative to clocks that are stationary in the reference frame, clocks in motion run slower, as do clocks in higher gravitational fields. In general, two synchronized clocks do not stay synchronized if they move relative to each other or undergo different gravitational forces. According to the classical Big Bang theory of cosmology, the universe has a finite past, having begun 13.7 billion years ago as spacetime expanded from an infinitesimal beginning. For an expanded discussion of these compressed remarks, see What Science Requires of Time.

5. What Kinds of Time Travel Are Possible?

Most philosophers and scientists believe time travel is possible. To define the term, we can say that in time travel, the traveler’s journey as judged by the traveler’s clock takes a different amount of time than the journey does as judged by the clocks of those who do not take the journey. That is, there is a difference between the traveler’s personal or proper time and the external or coordinate time of those who do not take the journey. The physical possibility of travel to the future is well accepted, but travel to the past is more problematical.

According to relativity theory, there are two ways to travel into the future using time dilation—either by moving at high speed or by taking advantage of the presence of an intense gravitational field. If you have a fast enough spaceship, you can travel into the future to the year 2,300 C.E. on Earth (as measured by Earth-based clocks and calendars) while your personal clock measures much less elapsed time. You can participate in that future, not just view it. But you can not get back to the twenty-first century on Earth by reversing your velocity.  See the twin paradox for the solution to the famous paradox involving time dilation. A second way to use time dilation to move into another person’s future is called gravitational time dilation. People who live in the ground floor apartment age slower than their twin who lives in the top floor of the same building.  So, a descending elevator is a time machine. The time travel is more noticeable if the younger twin lives near a black hole than simply nearer the Earth’s surface.

If you engage in either sort of travel to the future using time dilation, you do go to someone else’s future but you do not suddenly leap into anyone else’s future because your travel is continuous through time. Also, you are always in your own present during the time-traveling as judged by your personal time or proper time; and it is relations of mental and/or bodily continuity that constitute being the same person from one time to another.

Now, about travel to the past. In 1949, Kurt Gödel discovered a solution to Einstein’s field equations that allows continuous, closed future-directed timelike curves. To say this more simply, Gödel discovered that in some possible worlds that obey the theory of general relativity, you can eventually arrive into the past. In this unusual non-Minkowski spacetime, the universe as a whole is the time machine; no one needs to build a device in order to travel this way. In travel to the past, the traveler’s personal future (as judged by their proper time) becomes part of the universe’s past (as judged by cosmological time or coordinate time). Even more startling is that you may be able to travel into your own past, and perhaps meet yourself as a child or perhaps even become your earlier self. But, you can not change what has happened in the past. You can’t go back and prevent Adolf Hitler from gaining political power in Germany in the 1930s. You cannot kill your childhood self no matter how hard you try. In 1994, Kip Thorne provided a thought experiment in which a wormhole is manipulated to allow someone to suddenly appear in another person’s past or future.

Although time travel to the past apparently is physically possible, there are several well known arguments against the possibility. None are generally considered to be decisive. Here are the arguments:

  1. Time travel is impossible because if it were possible we should have seen many time travelers by now, but nobody has encountered any time travelers.
  2. And time travel is impossible because, if there were time travel, then when time travelers go back and attempt to change history they must always botch their attempts to change anything, and it will appear to anyone watching them at the time as if nature is conspiring against them. Since observers have never witnessed this apparent conspiracy of nature, there is no time travel.
  3. If there were travel to the past along a closed timelike curve, then these events would occur before themselves and after themselves, but this violates our definition of the word “before.”
  4. Travel to the past is impossible because it allows the gaining of information for free. For example, print out this article that you are reading. Enter a time machine and go back to a time when you can give me the article before I have ever thought about time travel. I then publish it as this article in this encyclopedia. This all seems to be consistent with relativity theory, but who first came up with the information in this article? You had it before I did, but you obtained it from me.
  5. Probing the possibility of a contradiction in backwards time travel, the American philosopher John Earman has described a rocket ship that carries a very special time machine. The time machine is capable of firing a probe into its own past. Suppose the ship is programmed to fire the probe on a certain date unless a safety switch is on. Suppose the safety switch is programmed to be turned on if and only if the “return” or “impending arrival” of the probe is (or has been) detected by a sensing device on the ship. Does the probe get launched? It seems to be launched if and only if it is not launched. Is this like saying, “I’ll design a gun that shoots if and only if it doesn’t shoot”? Not quite. The way out of Earman’s paradox may require us to accept that (a) somehow people will be unable to build the probe or the safety switch or an effective sensing device, or (b) time travel probes must go so far back in time that they never survive and make it back to the time when they were launched, or (c) time travel into the past is impossible.

These complaints are a mixture of arguments that time travel is not logically possible, that it not physically possible, and that it is unlikely, given the empirical evidence. Perhaps it will be helpful to explain what is going on in thought experiments that are designed to illustrate the possibility of time travel. The possibility we have in mind here is either logical possibility or physical possibility. When we explore the logical possibility of time travel we are permitted to change current technology and the current principles of science but not to change a law of logic. A situation in which your grandfather is born and not born is not logically possible because it violates the law of logic called the law of non-contradiction. The law that for any existing thing there is a sufficient reason or cause for why it exists was called a law of logic by Leibniz but is not considered a law of logic today, but only an interesting principle used in metaphysics. Physical possibility, as opposed to logical possibility, is logical consistency with all the physical laws. When we explore the physical possibility of time travel we must not change any laws of logic nor any of our accepted laws of science. It is logically possible for an astronaut to fly faster than the speed of light and for an acorn to grow to become a carrot rather than an oak tree, but these situations are not physically possible because they violate laws of relativity and evolution. It is physically possible, but beyond the capability of current technology, to expand a wormhole to six feet wide and to travel back in time and meet your younger self.

For more discussion of time travel, see the encyclopedia article “Time Travel.”

6. Does Time Require Change? (Relational vs. Substantival Theories)

Substantival theories are theories that imply time is substance-like in that it exists independently of the spacetime relations exhibited by physical processes. Relational theories imply time’s existence requires there to be some physical process in the universe–such as an electron’s movement or a change in a field. Some substantival theories describe spacetime as being like a container for events. The container exists with or without events in it. Relational theories imply there is no container without contents. But the substance that substantivalists have in mind is more like a medium pervading all of spacetime and less like an external container. John Norton’s metaphors might help. Our universe is like a painting, and substantival spacetime is like the painter’s canvas. If you take away the paint (the spacetime events) from the painting, you still have the canvas. Relational spacetime is like citizenship. Take away the citizens (the spacetime events), and you have no citizenship left. When the relational theory says change is necessary for time to exist, what is meant by “change” is first-order change, not second-order change. That is, the second-order change that occurs when Queen Anne’s death recedes ever farther into the past does not count as the kind of change emphasized by the relational theory. Its snowing on her grave does count.

Everyone agrees time cannot be measured without there being changes, but the present issue is whether it exists without changes. The substantival theories are theories that spacetime could exist even if there were no physical objects and events in the universe. Relational theories, on the other hand, imply that spacetime is nothing but the spatiotemporal relationships among possible objects and their possible events. Relational theories are also called “relationalist” theories. Substantival theories are sometimes called “absolute theories.” Unfortunately the term “absolute theory” is used in two other ways. The term is often used to emphasize that spacetime is immutable in the sense of not changing its properties. And it is used to suggest that time is independent of observer or reference frame. Although Einstein’s theory implies there is no absolute time in these other two ways (immutable and independent of reference frame), it is an open question whether relativity theory supports the relational theory in the primary sense of that term.

The first advocate of a relational theory of time was Aristotle. He said, “neither does time exist without change.” [Physics, 218b] However, the battle lines were most clearly drawn in the early 18th century when Leibniz argued for the relational position against Newton, who had adopted a substantival theory of time. Leibniz’s principal argument against Newton is a reductio ad absurdum. Suppose Newton’s space and time were to exist. But one could then imagine a universe just like ours except with everything shifted five miles east and five minutes earlier. However, there would be no reason why this shifted universe does not exist and ours does. Now we have arrived at a contradiction because, if there is no reason for there to be our universe over the shifted universe, then we have violated Leibniz’s Principle of Sufficient Reason: that there is an understandable reason for everything being the way it is. So, by reductio ad absurdum, Newton’s substantival space and time do not exist. In short, the trouble with Newton’s theory is that it leads to too many unnecessary possibilities.

Newton offered this two-part response: (1) Leibniz is correct to accept the Principle of Sufficient Reason regarding the rational intelligibility of the universe, but there do not have to be knowable reasons for humans; God might have had His own sufficient reason for creating the universe at a given place and time even though mere mortals cannot comprehend His reasons. (2) The bucket thought-experiment shows that acceleration relative to substantival space is detectable; thus substantival space is real, and if substantival space is real, so is substantival time. Suppose we tie a bucket’s handle to a rope hanging down from a tree branch. Partially fill the bucket with water, and let it come to equilibrium. Notice that there is no relative motion between the bucket and the water, and in this case the water surface is flat. Now spin the bucket, and keep doing this until the angular velocity of the water and the bucket are the same. In this second case there is also no relative motion between the bucket and the water, but now the water surface is concave. So spinning makes a difference, but how can a relational theory explain the difference in the shape of the surface? It can not, says Newton. When the bucket and water are spinning, what are they spinning relative to? Because we can disregard the rest of the environment including the tree and rope, says Newton, the only explanation of the difference in surface shape between the non-spinning case and the spinning case is that when it is not spinning there is no motion relative to space, but when it is spinning there is motion relative to space itself, and thus space itself is acting upon the water surface to make it concave. Alternatively expressed, the key idea is that the presence of centrifugal force is a sign of rotation relative to substantival space. Leibniz had no rebuttal. So, for over two centuries thereafter, Newton’s substantival theory of space and time was generally accepted by European scientists and philosophers.

One hundred years later, Kant entered the arena on the side of Newton. In a space containing only a single glove, said Kant, Leibniz could not account for its being a right-handed glove versus a left-handed glove because all the internal relationships would be the same in either case. However, we all know that there is a real difference between a right and a left glove, so this difference can only be due to the glove’s relationship to space itself. But if there is a “space itself,” then the substantival theory is better than the relational theory.

Newton’s theory of time was dominant in the 18th and 19th centuries, even though during those centuries Huygens, Berkeley, and Mach had entered the arena on the side of Leibniz. In the 20th century, Reichenbach and the early Einstein declared the special theory of relativity to be a victory for the relational theory. Special relativity, they said, ruled out a space-filling ether, the leading candidate for substantival space, so the substantival theory was incorrect. And the response to Newton’s bucket argument is to note Newton’s error in not considering the environment. Einstein agreed with Mach that, if you hold the bucket still but spin the background stars, the water will creep up the side of the bucket and form a concave surface. Although it was initially thought by Einstein and others that relativity theory supported Mach, Lawrence Sklar (Sklar, 1976, pp. 219-21) argues that this may not be correct.

Many philosophers argue that Reichenbach and the early Einstein have been overstating the amount of metaphysics that can be extracted from the physics. Remember the ambiguity in “substantival” mentioned above? There is substantival in the sense of independent of reference frame and substantival in the sense of independent of events. Which sense is ruled out when we reject a space-filling ether? The critics admit that general relativity does show that the curvature of spacetime is affected by the distribution of matter, so today it is no longer plausible for an absolutist to assert that the “container” is independent of the matter it contains. But, so they argue, general relativity does not rule out a more sophisticated substantival theory–to be discussed below. By the end of the 20th century, substantival theories had gained some ground.

In 1969, Sydney Shoemaker presented an argument to convince us of the understandability of time existing without change, as Newton’s absolutism requires. Divide space into three disjoint regions, called region 3, region 4, and region 5. In region 3, change ceases every third year for one year. People in regions 4 and 5 can verify this and convince the people in region 3 after they come back to life at the end of their frozen year. Similarly, change ceases in region 4 every fourth year for a year; and change ceases in region 5 every fifth year. Every sixty years, that is, every 3 x 4 x 5 years, all three regions freeze simultaneously for a year. In year sixty-one, everyone comes back to life, time having marched on for a year with no change. But philosophers of time point out that, even if Shoemaker’s scenario shows time’s existing without change is understandable, the deeper question is whether time does exist without change.

Here is one argument that it does. Must the relationist say there can be no “empty” time? If events occur in a room before and after 11:01 AM, but not exactly at 11:01 AM, must the relationalist say there never was a time of 11:01 AM in the room? To avoid saying “yes,” which would be absurd, a relationalist might say 11:01 exists in the room and everywhere else because somewhere outside the room something is happening then, and somehow or other sense can be made of time in the room in terms of these external events. The absolutist then asks us to consider the possibility that the room is the whole universe. In that case, the relationalist response to losing 11:01 AM would probably be to say possible events occur then in the room even if actual events do not. But now look where we are, says the absolutist. If the relational theory is going to consider spacetime points to be permanent possibilities of the location of events, then the relational theory collapses into substantivalism. This is because, to a substantivalist, a spacetime point is also just a place where something could happen.

Hartry Field offers another argument for the substantival theory by pointing out that modern physics requires gravitational and electromagnetic fields that cover spacetime–a light wave, say, is considered to be a ripple in the field. The fields are states of spacetime, with the field having a value (a number or vector) at points throughout the field. These fields cannot be states of some Newtonian ether, but there must be something to have the field properties. What else except substantive spacetime points?

Another criticism goes like this. For the relational theory, all that exists are physical objects and their relationships, so its temporal continuum is just a useful fiction created by mathematical abstraction from what really exists. Since this continuum is not just a fiction, we should reject the relational theory.

7. Does Time Flow?

“It is as if we were floating on a river, carried by the current past the manifold of events which is spread out timelessly on the bank,” said one philosopher trying to capture time’s flow with a helpful metaphor. Santayana offered another: “The essence of nowness runs like fire along the fuse of time.” The philosopher’s goal is to clarify the idea of time’s flow, the passage of time. Everyone agrees that time appears to flow, but not everyone agrees that it actually does.

There are two categories of theories of time’s flow. The first, and most popular among physicists, is that the flow is an illusion, the product of a faulty metaphor. Time exists, things change, but time does not flow objectively. There may well be some objective feature of our brains that causes us to believe we are experiencing a flow of time, but the flow itself is not objective. It is as subjective as the feeling that there is a here as opposed to a there. This kind of theory is often characterized as a “myth-of-passage” theory. It is more likely to be adopted by those who believe McTaggart’s B-series is more fundamental than his A-series.

The second category of theories of time’s flow are the dynamic theories of time, which imply that the flow is objective, a feature of our mind-independent reality that is to be found in, say, today’s  scientific laws, or, if it has been missed there, then in future scientific laws. A dynamic theory is closer to common sense, and has historically been the more popular theory among philosophers.

One dynamic theory implies that the flow is a matter of events changing from being indeterminate in the future to being determinate in the present and past. Time’s flow is really events becoming determinate, so dynamic theorists speak of time’s flow as “temporal becoming.” A second dynamic theory implies that the flow is a matter of events changing from being future, to being present, to being past. This is the kind of flow associated with McTaggart’s A-series of events.

Opponents of these two dynamic theories complain that when events change in these senses, the change is not a real change in the event’s essential, intrinsic properties, but only in the event’s relationship to the observer. For example, saying the death of Queen Anne is an event that changes from present to past is no more of a real change in the event than saying her death changed from being approved of to being disapproved of. This extrinsic change in approval does not count as a real change in her death, and neither does the so-called second-order change from present to past or from indeterminate to determinate. Attacking the notion of time’s flow in this manner, Grünbaum said: “Events simply are or occur…but they do not ‘advance’ into a pre-existing frame called ‘time.’ … An event does not move and neither do any of its relations.”

A third dynamic theory says time’s flow is the coming into existence of facts, the actualization of new states of affairs, but unlike the first dynamic theory there is no commitment to events changing. A fourth dynamic theory suggests the flow is reflected in the change over time of truth values of declarative sentences or proposition. For example, the sentence “It is now raining” was true during the rain yesterday but has changed to false on today’s sunny day. It is these sorts of truth value changes that are at the root of time’s flow. In response, critics suggest that the indexical (or token reflexive) sentence “It is now raining” has no truth value because the reference of “now” is unspecified. If it can not have a truth value, it can not change its truth value. However, the sentence is related to a sentence that does have a truth value. Supposing it is now midnight here on April 1, 2007, and the speaker is in Sacramento, California, then the indexical sentence “It is now raining” is related to the more complete or context-explicit sentence “It is raining at midnight on April 1, 2007 in Sacramento, California.” Only these non-indexical, non-context-dependent, complete sentences have truth values, and these truth values do not change with time. So, fully-described events do not change their properties because complete or “eternal” sentences do not change their truth values.

There are other dynamic theories of time. John Norton (Norton, 2010) argues that time’s flow is objective but so far is beyond the reach of our understanding. Tim Maudlin argues that the objective flow of time is fundamental and unanalyzable. He is happy to say “time does indeed pass at the rate of one hour per hour.” (Maudlin, 2007, p. 112)

Regardless of how we analyze the metaphor of time’s flow we also need to analyze the metaphor of time’s having a direction—the arrow of time.

8. What Gives Time Its Direction or Arrow?

Time’s arrow is the way processes go over time, and that way is the direction of disarray, the direction toward equilibrium. The arrow can be seen in the process of making an omelet. We get omelets from eggs; we never get eggs from omelets. Or consider mixing cool cream into hot, black coffee. We soon get lukewarm, brown coffee, but we never notice the reverse process of lukewarm, brown coffee separating into cool cream and black coffee. Such is the way these two irreversible thermodynamic processes go. The arrow of a physical process is the way it normally goes, the way it normally unfolds through time. If a process goes only one-way, we call it an irreversible process; otherwise it is reversible. Strictly speaking, a reversible process is one that is reversed by an infinitesimal change of its surrounding conditions, but we can overlook this fine point because of the general level of the present discussion. Also, strictly speaking being irreversible means we cannot reconstruct the past from knowledge of the current state. At any rate, the amalgamation of the universe’s irreversible processes produces the cosmic arrow of time, the master arrow. Usually this arrow is what is meant when one speaks simply of “time’s arrow.” So, time’s arrow indicates directed processes in time and may or may not have anything to do with the flow of time. How to explain the arrow is still an open question in science and philosophy.

Because so many of the physical processes we commonly observe do have an arrow, you might think that an inspection of the basic physical laws would readily reveal time’s arrow. It will not. With some exceptions, such as the collapse of the quantum mechanical wave function, all the basic laws of fundamental processes are time symmetric.  This means that if a certain process is allowed by the laws, then that process reversed in time is also allowed, and, all other things being equal, either direction is as probable as the other. Maxwell’s equations of electromagnetism, for example, are basic laws, and they can be used to predict that television signals can exist, but the equations do not tell us whether those signals arrive before or arrive after they are transmitted. In other words, these basic laws of science do not by themselves imply an arrow of time.

a. What Needs to be Explained

There are many goals for a fully developed theory of time’s arrow. It should tell us (1) why time has an arrow; (2) why the basic laws of science do not reveal the arrow, (3) why the arrow is apparent in macro processes but not micro processes; (4) why entropy increases in the future rather than decreases even though the decrease is physically possible given current basic laws; (5) what it would be like for the arrow to reverse direction; (6) what are the characteristics of a physical theory that would pick out a preferred direction in time; (7) what the relationships are among the various more specific arrows of time–the various kinds of temporally asymmetric processes such as entropy increases [the thermodynamic arrow], causes preceding their effects [the causal arrow], light radiating away from hot objects rather than converging into them [the electromagnetic arrow], and our knowing the past more easily than the future [the knowledge arrow].

b. Explanations or Theories of the Arrow

According to physicists, although they don’t universally agree on this, the most likely explanation of the emergence of an arrow of time in a world with time-blind basic laws is that the arrow is a product of the way entropy changes, and entropy changes are due to, among other things, the state of the universe at the time of the Big Bang.

There are many useful definitions of entropy. It is a measure inversely related to the energy available for work in a physical system. According to another definition, the entropy of a physical system isolated from external influences is a measure [specifically, the logarithm] of how many microstates are macroscopically indistinguishable. Less formally, entropy can be defined as being a measure of the disorganization of the system. More entropy implies more disorganization. According to the 2nd Law of Thermodynamics, entropy change in the future is almost always entropy increase, so the change in entropy is a one-way street toward greater disorganization and less useful forms of energy. When a car burns gasoline, the entropy increase is evident in the fact that the new heat energy distributed throughout the byproducts of  the gasoline combustion is much less useful than was the potential chemical energy in the pre-combustion gasoline. Entropy  in a system such as the gas in a cubic box increases for a few minutes then stops changing because the system  reaches equilibrium, but the entropy of our universe has been increasing for the last 13.7 billion years and will continue to do so for a very long time. At the time of the Big Bang event, the universe was in a highly organized, low-entropy state, and it has been running down and getting more disorganized ever since. This running down is the cosmic arrow of time.

According to the 2nd Law of Thermodynamics, which is not a basic law of physics but rather a derived one, if an isolated system with a great many particles is not in equilibrium, then it is overwhelmingly likely that the system’s entropy will increase in the future. But, and here is the main difficulty, surprisingly it is just as likely that the system also had higher entropy in the past—as described by the red line in the diagram below. Yet we know our universe is an isolated system, and it surely did not have high entropy in the past—at least not in the past that is between now and the Big Bang event—so the low value of entropy in the past is puzzling. Sean Carroll (2010) offers a simple illustration of the red line problem. If you found a half-melted ice cube in an isolated glass of water (the black dot in the diagram), and all you otherwise knew about the universe is that it obeys our current, basic laws, then you’d predict that the ice cube would melt into a liquid in the future (solid green line). But similarly you also would infer that your glass evolved from a state of  liquid water (red line). You would not infer that the present half-melted state evolved from a state where the glass has a solid cube in it (dashed green line), yet it did. In order to predict the dashed green line rather than the dashed red line, physicists have found it necessary to adopt the Past Hypothesis—that the universe began in a state of very low entropy. That is, if the Past Hypothesis is true, then the most probable history of the universe over the last 13.7 billion years is one in which entropy rises because it started off so improbably low.

graph of entropy vs. time

Why was entropy so low at the time of the Big Bang? One suggestion is that it was low because entropy had to have been increasing after that due to the universe’s spatial expansion since in an expanding universe the entropy increases. That is, if a non-expanding universe or any other isolated system were to completely run down and reach maximum entropy it would reach equilibrium and lose its arrow of time, but the universe actually is expanding, and an expanding space allows entropy to increase even if the universe was at an equilibrium maximum at the Big Bang, before expansion.

No explanation of why entropy was so low at the time of the Big Bang has yet satisfied the majority of experts, although they agree that the relative smoothness in temperature differences in the early universe is evidence of the very low entropy of the early universe. But did spatial expansion or something else cause this low entropy? Some physicists (for example, Richard Feynman) and philosophers (for example, Craig Callender) say it may simply be a brute fact—that is, there is no causal explanation for the low entropy beginning. Objecting to inexplicable initial facts as being unacceptably ad hoc, the physicists Walther Ritz and Roger Penrose say we must not yet have found the true laws (or invented the best laws) underlying nature’s behavior. We need to keep looking for basic, time asymmetrical laws in order to account for the initial low entropy and thus for time’s arrow.

The low entropy appears to be due to the early universe’s having just the right amount of homogeneity or smoothness of temperature differences so that galaxies would eventually form. If it were initially smoother, then there would be no congealing of matter into galaxies; if it were initially less smooth, then most all the matter would have long ago congealed into large black holes. So, the issue of how to explain the arrow is deeply connected to the issue of why the early universe had just the right smoothness.

c. Multiple Arrows

The past and future are different in many ways that reflect the arrow of time. Consider the difference between time’s arrow and time’s arrows. The direction of entropy change is the thermodynamic arrow. Here are some suggestions for additional arrows:

  1. We remember last week, not next week.
  2. There is evidence of the past but not of the future.
  3. Our present actions affect the future and not the past.
  4. It is easier to know the past than to know the future.
  5. Radio waves spread out from the antenna, but never converge into it.
  6. The universe expands in volume rather than shrinks.
  7. Causes precede their effects.
  8. We see black holes but never white holes.
  9. B meson decay, neutral kaon decay, and Higgs boson decay are each different in a time reversed world.
  10. Quantum mechanical measurement collapses the wave function.
  11. Possibilities decrease as time goes on.

Most physicists suspect all these arrows are linked so that we can not have some arrows reversing while others do not. For example, the collapse of the wave function is generally considered to be due to an increase in the entropy of the universe. It is also well accepted that entropy increase can account for the fact that we remember the past but not the future, that effects follow causes rather than precede them, and that animals grow old and never young. However, the linkage of all the arrows may require as yet undiscovered laws. And even if all arrows are produced by entropy flow, the origin of the initial low entropy is still a mystery. Perhaps if we explore the past farther back beyond the big bang event, we will find that entropy then was high also, but for some reason reached a low point at the time of our big bang [see Carroll, 2010]. Carroll speculates that the truly highest-entropy configuration in the very, very distant past is one where space is not inhomogeneous but is essentially empty of everything except vacuum energy.

d. Reversing the Arrow

Could the cosmic arrow of time have gone the other way? Most physicists suspect that the answer is yes, and they say it could have gone the other way if the initial conditions of the universe at the Big Bang event had been different. Crudely put, if all the particles’ trajectories and charges are reversed, then the arrow of time must reverse. A few physicists and philosophers have speculated that the arrow might reverse in our future. In this scenario, time would lose its unidirectionality as the universe approaches a state of equilibrium, but eventually the universe would evolve away from equilibrium in which the directional processes now go in the reverse order to the way they went before the reversal. This new era would be an era of reversed time, and there would be a period of non-directional time separating the two eras.

If the cosmic arrow of time were to reverse this way, perhaps our past would be re-created and lived in reverse order. This re-occurrence of the past is different than the re-living of past events via time travel. With time travel the past is re-visited in the original order, not in reverse order.

Philosophers have asked interesting questions about the reversal of time’s arrow. What does it really mean to say time reverses? Would entropy flow change from increasing to decreasing [since if entropy continually increased as time reversed then a big crunch could not be the big bang in reverse]? If time were to be going in reverse only in some far off corner of the universe, would dead people there become undead, and would the people there walk backwards up steps while remembering the future? First off, would it even be possible for them to be conscious? Assuming consciousness is caused by brain processes, could there be consciousness if their nerve pulses reversed, or would this reversal destroy consciousness? Supposing the answer is that they would be conscious, would people in that far off corner appear to us to be pre-cognitive if we could communicate with them? Would the feeling of being conscious be different for time-reversed people? [Here is one suggestion. There is one direction of time they would remember and call “the past,” and it would be when the entropy is lower. That is just as it is for us who do not experience time-reversal.] If Aristotle were correct that the future, unlike the past, is undetermined or open, then wouldn’t the future of people in the time-reversed region be open, too? But it is like our past, so what should we conclude from this? Should we conclude that our own past might really be undetermined and open, too, that is, that our past could change? And there are other questions. Consider communication between us and the inhabitants of that far off time-reversed region of the universe. If we sent a signal to the time-reversed region, could our message cross the border, or would it dissolve there, or would it bounce back? If residents of the time-reversed region successfully sent a recorded film across the border to us, should we play it in the ordinary way or in reverse? Would any interaction between their region and ours upset their delicately constructed world and cause their entropy to increase?

9. Is Only the Present Real?

a. Presentism, the Growing Past, and the Block Universe

Have past objects, such as dinosaurs, slipped out of existence? More generally, we are asking whether the past is real. How about the future? Philosophers are divided into three camps on the question of the reality of the past, present, and future. The presentist viewpoint maintains that the past and the future are not real, and that only the present is real, so if a statement about the past is true, this is because some present facts make it true. Advocates of a growing past argue that, in addition to the present, the past is also real. Reality “grows” with the coming into being of determinate reality from an indeterminate or potential reality. “The world grows by accretion of facts,” says Richard Jeffrey. Aristotle (in De Interpretatione, chapter 9) and C. D. Broad advocated a growing-past theory. Parmenides, Duns Scotus and A. N. Prior are presentists.

Opposing both presentism and the growing past theory, Bertrand Russell, J.J.C. Smart, W.V.O. Quine, Adolf Grünbaum, and Paul Horwich object to assigning special ontological status to the present. They say there is no objective ontological difference among the past, the present, and the future just as there is no objective ontological difference among here, there, and far. Yes, we thank goodness that the pain is there rather than here, and past rather than present, but these differences are subjective, being dependent on our point of view. This ontology of time is called the block universe theory because it regards reality as a single block of spacetime with its time slices ordered by the temporally-before relation. It is mental perspectives only that divide the block into a past part, a present part, and a future part. The future, by the way, is the actual future, not all possible futures. William James coined the term “block universe,” but the theory is also called “eternalism” and the “static theory of time.” By the way, if time has an infinite future or past, or if space an infinite extent, then the block is infinitely large.

Although presentists say dinosaurs are not real, whereas eternalists say that dinosaurs are as real as anything in the present, another camp of philosophers argue that the presentist-eternalist debate is merely verbal because each side is using the word “real” in a different sense; the presentist uses it in a tensed sense, whereas the eternalist uses it in an untensed sense.

The biggest challenge for presentists is to account for change. The presentist somehow must distinguish between last week and three weeks ago. The presentist also is challenged to explain the notion of an object’s having a speed, which is normally explained by saying the object has a different location than it just had in the very recent past.

The presentist and the advocate of the growing past will usually unite in opposition to the block universe (eternalism) on the grounds that it misses the special “open” character of the future and the equally significant point that the present is so much more vivid to a conscious being than is any other time-slice of spacetime.

Another common argument against the block universe is that according to it there can be only one future, so this is fatalism, and we know fatalism is incorrect. The counter from the defenders of the block universe is that even though there will be only one future there might be many different futures for all we know. Another less common argument against the block universe is that it implies the past is real in a changeless, static sense. So that means that past wars are still being fought, which is absurd. The counter from the defenders of the block universe is that their view implies past wars are still being fought only in the tenseless sense of “are,” so the critic is equivocating on the word “are.”

The advocates of the block universe counter that only the block universe can make sense of relativity’s implication that, if people are in certain relative motions, an event in person A’s present can be in person B’s future. Presentism and the growing-past theories must suppose that this event is both real and unreal because it is real for A but not real for B. Surely that conclusion is unacceptable, they claim. Their two key assumptions here are that relativity does provide an accurate account of the spatiotemporal relations among events, and that if there is some frame of reference in which two events are simultaneous, then if one of the events is real, so is the other.

Opponents of the block universe charge that it does not provide an accurate account of the way things are because it leaves out “the now” or “the present.” This metaphysical dispute about a spatially extended present was fueled by Einstein who said:

Since there exists in the four dimensional structure no longer any slices which represent “now” objectively…it appears more natural to think of physical reality as a four dimensional existence instead of, as hitherto, the evolution of a three dimensional existence.

Many philosophers, however, do not agree with Einstein.

b. Enduring and Perduring Objects

One implication of the block universe theory is that events are the basic objects of the universe. These are not three-dimensional but rather four-dimensional. Just as all of spacetime is a four-dimensional block, so also basic objects are four-dimensional sub-blocks. Traditionally an adult human being is a three-dimensional object existing wholly at an instant, but for the four-dimensionalist, the human being consists of its childhood and its middle age and thus exists over a time period rather than only at a time. To prolong a tennis match is to elongate its four-dimensional block along the time axis. Objects considered four-dimensionally are said to be “perduring objects” as opposed to the three-dimensional “enduring objects” of common sense.

c. Truth Values and Free Will

This philosophical dispute has taken a linguistic turn by focusing upon a question about language: “Are predictions true or false at the time they are uttered?” Those who believe in the block universe (and thus in the determinate reality of the future) will answer “Yes” while a “No” will be given by presentists and advocates of the growing past. The issue is whether contingent sentences uttered now about future events are true or false now rather than true or false only in the future at the time the predicted event is supposed to occur.

Suppose someone says, “Tomorrow the admiral will start a sea battle.” And suppose that tomorrow the admiral orders a sneak attack on the enemy ships. And suppose that this action starts a sea battle. Advocates of the block universe argue that, if so, then the above sentence was true all along. Truth is eternal or fixed, they say, and “is true” is a tenseless predicate, not one that merely says “is true now.” These philosophers point favorably to the ancient Greek philosopher Chrysippus who was convinced that a contingent sentence about the future is true or false, and it can not be any value in between such as “indeterminate.” Many others, following a suggestion from Aristotle, argue that the sentence is not true until it can be known to be true, namely at the time at which the sea battle occurs. The sentence was not true before the battle occurred. In other words, predictions have no (classical) truth values at the time they are uttered. Predictions fall into the “truth value gap.” This position that contingent sentences have no classical truth values is called the Aristotelian position because many researchers throughout history have taken Aristotle to be holding the position in chapter 9 of On Interpretation–although today it is not so clear that Aristotle himself held it.

The principal motive for adopting the Aristotelian position arises from the belief that if sentences about future human actions are now true, then humans are determined to perform those actions, and so humans have no free will. To defend free will, we must deny truth values to predictions.

The Aristotelian argument against predictions being true or false has been discussed as much as any in the history of philosophy [See "Logical Determinism" in the Free Will article], and it faces a series of challenges. First, if there really is no free will, or if free will is compatible with determinism, then the motivation to deny truth values to predictions is undermined.

Second, according to the compatibilist, your choices affect the world, and if it is true that you will perform an action in the future, it does not follow that now you will not perform it freely, nor that you are not free to do otherwise if your intentions are different, but only that you will not do otherwise. For more on this point about modal logic, see Foreknowledge and Free Will.

A third challenge arises from moral discussions about the interests of people who are as yet unborn. Quine argues that if we have an obligation to conserve the environment for these people, then we are treating them as being as real as the people around us now. Only the block universe view can make sense of this treatment.

A fourth challenge, from Quine and others, claims the Aristotelian position wreaks havoc with the logical system we use to reason and argue with predictions. For example, here is a deductively valid argument:

There will be a sea battle tomorrow.

If there will be a sea battle tomorrow, then we should wake up the admiral.

So, we should wake up the admiral.

Without the premises in this argument having truth values, that is, being true or false, we cannot properly assess the argument using the usual standards of deductive validity because this standard is about the relationships among truth values of the component sentences–that a valid argument is one in which it is impossible for the premises to be true and the conclusion to be false. Unfortunately, the Aristotelian position says that some of these component sentences are neither true nor false, so Aristotle’s position is implausible.

In reaction to this fourth challenge, proponents of the Aristotelian argument claim that if Quine would embrace tensed propositions and expand his classical logic to a tense logic, he could avoid those difficulties in assessing the validity of arguments that involve sentences having future tense.

Quine has claimed that the analysts of our talk involving time should in principle be able to eliminate the temporal indexical words because their removal is needed for fixed truth and falsity of our sentences [fixed in the sense of being eternal sentences whose truth values are not relative because the indicator words have been replaced by times, places and names, and whose verbs are treated as tenseless], and having fixed truth values is crucial for the logical system used to clarify science. “To formulate logical laws in such a way as not to depend thus upon the assumption of fixed truth and falsity would be decidedly awkward and complicated, and wholly unrewarding,” says Quine.

Philosophers are still very divided on the issues of whether only the present is real, what sort of deductive logic to use, and whether future contingent sentences have truth values.

10. Are There Essentially-Tensed Facts?

All the world’s cultures have a conception of time, but in only half the world’s languages is the ordering of events expressed in the form of tense (Pinker, p. 189). The English language, for example, expresses conceptions of time with tenses but also in other ways, such as with adverbial time phrases such as “now,” “tomorrow” and “twenty-three days ago.” Philosophers have asked what we are basically committed to when we locate an event in the past, in the present, or in the future. For example, how should we understand the past tense verb in, “Mohammed’s birth occurred centuries ago”? There are two major answers. One answer is that tense distinctions represent objective features of reality that are not captured by the popular block universe approach. This answer takes tenses very seriously and is called the tensed theory of time, or the A-theory in McTaggart’s sense of A vs. B. A second answer to the question of the significance of tenses is that they are subjective features of the perspective from which the subject views the universe. Actually this disagreement isn’t really about tenses in the grammatical sense, but about the significance of the distinctions of past, present, and future which those tenses are used to mark.

On the tenseless theory of time, or the B-theory, whether the birth of Mohammed occurred there depends on the speaker’s perspective; similarly, whether the birth occurs then is equally subjective. The proponent of the tenseless view does not deny the importance or coherence of talk about the past, but will say it really is (or should be analyzed as being) talk about our own relation to events. My assertion that Mohammed’s birth has occurred might be analyzed as asserting that the birth event happens before the event of my writing this sentence.

This controversy is often presented as a dispute about whether tensed facts exist, with advocates of the tenseless theory objecting to tensed facts such as the fact of Mohammed’s having been born. The primary function of tensed facts is to make tensed sentences true. For the purposes of explaining that point, let us uncritically accept the Correspondence Theory of Truth and apply it to the following past tense sentence:

Custer died in Montana.

If we apply the Correspondence Theory directly to this sentence, then the tensed theory would imply

The sentence “Custer died in Montana” is true because it corresponds to the tensed fact that Custer died in Montana.

Opponents of tensed facts argue that the Correspondence Theory should be applied only indirectly. One approach, the classical tenseless approach, argues that the Correspondence Theory should be applied only to the result of analyzing away tensed sentences into equivalent sentences that do not use tenses. They might say that the sentence “Custer died in Montana” has this equivalent “eternal” sentence:

There is a time t such that Custer dies in Montana at time t, and time t is before the time of the writing of the sentence “Custer died in Montana” by Dowden in the article “Time” in The Internet Encyclopedia of Philosophy.

In this analysis, the verb dies is logically tenseless (although grammatically it is present tensed). Applying the Correspondence Theory to this new sentence yields:

The sentence “Custer died in Montana” is true because it corresponds to the tenseless fact that there is a time t such that Custer dies in Montana at time t, and time t is before the time of the utterance (or writing) of the sentence “Custer died in Montana” by Dowden in the article “Time” in The Internet Encyclopedia of Philosophy.

This analysis does not require tensed facts. The analysis is challenged on the grounds that it can succeed only for utterances or inscriptions, but a sentence can be true even if never uttered or written by anyone.

There are other challenges. Roderick Chisholm and A. N. Prior claim that the word “is” in the sentence “It is now midnight” is essentially present tensed because there is no translation using only tenseless verbs. Trying to analyze it as, say, “There is a time t such that t = midnight” is to miss the essential reference to the present in the original sentence because the original sentence is not always true, but the sentence “There is a time t such that t = midnight” is always true. So, the tenseless analysis fails. There is no escape by adding “and t is now” because this last indexical still needs analysis, and we are starting a vicious regress.

Earlier, Prior [1959] had argued that after a painful event,

one says, e.g., “Thank goodness that’s over,” and [this]…says something which it is impossible that any use of a tenseless copula with a date should convey. It certainly doesn’t mean the same as, e.g., “Thank goodness the date of the conclusion of that thing is Friday, June 15, 1954,” even if it be said then. (Nor, for that matter, does it mean “Thank goodness the conclusion of that thing is contemporaneous with this utterance.” Why should anyone thank goodness for that?).

D. H. Mellor, who advocates a newer subjective theory of tenses, says the truth conditions of any tensed sentence can be explained without tensed facts even if Chisholm and Prior are correct that some tensed sentences can not be translated into tenseless ones. If I am speaking to you and say, “It is now midnight,” then the conditions under which this is true are that my utterance of “It is now midnight” occurs at the same time as your hearing the utterance, which in turn is the same time as when our standard clock declares the time to be midnight in our reference frame. Notice that no tensed facts were appealed to in the explanation of those truth conditions. Mellor would say it is not the pastness of the painful event that explains why I say, “Thank goodness that’s over.” My gladness is explained by my belief that the event is past, plus its being true that the time of the occurrence of that utterance is greater than the time of the occurrence of the painful event. In addition, tenseless sentences can be used to explain the logical relations between tensed sentences: that one tensed sentence implies another, is inconsistent with yet another, and so forth. And understanding truth conditions and truth implications is the main thing you know when you understand a declarative sentence. In other words, the meaning of tensed sentences can be explained without utilizing tensed properties or tensed facts. Then Ockham’s Razor is applied. If we can do without essentially-tensed facts, then we should say essentially-tensed facts do not exist. To summarize, tensed facts were presumed to be needed to account for the truth of tensed talk; but the analysis shows that ordinary tenseless facts are adequate. So, there are no essentially-tensed facts, according to Mellor.

11. What is Temporal Logic?

Temporal logic is the representation of information about time by using the methods of symbolic logic to formalize which statements (propositions, sentences) about time imply which others. The classical approach to temporal logic is via tense logic, a formalism that adds tense operators to an existing system of symbolic deductive logic. The pioneer in the late 1950s was A. N. Prior. He created a new symbolic logic to describe our use of time words such as “now,” “happens before,” “afterwards,” “at all times,” and “sometimes.” Prior assumes that a proposition such as “Socrates is sitting down” can be true at one time and false at another time. That assumption is challenged by some philosophers such as W.V. Quine, who prefers to think of propositions as being timelessly true or timelessly false.

Prior was the first to appreciate that time concepts are similar in structure to modal concepts such as “it is possible that” and “it is necessary that,” and so he adapted modal propositional logic for his tense logic. Dummett and Lemmon also made major, early contributions to tense logic.

One standard system of tense logic is a variant of the S4.3 system of modal logic. In this formal tense logic, the usual modal operator “it is possible that” is re-interpreted to mean “at some past time it was the case that.” Let the letter “P” represent this operator, and add to the axioms of classical propositional logic the modal-like axiom P(p v q) iff Pp v Pq. The axiom says that for any two present-tensed propositions p and q, at some past time it was the case that p or q if and only if either at some past time it was the case that p or at some past time it was the case that q. The S4.3 system’s key axiom is the equivalence

Pp & Pq iff P(p & q) v P(p & Pq) v P(q & Pp).

This axiom captures part of our ordinary conception of time as a linear succession of states of the world. Another axiom might state that if proposition q is true, then it will always be true that q has been true at some time. Prior and others have suggested a wide variety of axioms for tense logic, but logicians still disagree about what axioms are needed to make correct beliefs about time be theorems that are logical consequences of those axioms. Some extension of classical tense logic is definitely needed in order to express “q has been true for the past three days.”

The concept of being in the past is usually treated by metaphysicians as a predicate that assigns properties to events, but, in the tense logic just presented, the concept is treated as an operator P upon propositions, and this difference in treatment is objectionable to some metaphysicians.

The other major approach to temporal logic does not use a tense logic. Instead, it formalizes temporal reasoning within a first-order logic without modal-like tense operators. This so-called method of “temporal arguments” adds an additional variable, a time argument, to any predicate involving time in order to indicate how its satisfaction depends on time. A predicate such as “is less than seven” does not involve time, but the predicate “is resting” does. If “x is resting” is represented classically as R(x), where R is a one-argument predicate, then it would be represented in temporal logic as R(x,t) and would be interpreted as saying x has property R at time t. R has been changed to a two-argument predicate by adding a “temporal argument.” The time variable “t” is treated as a new sort of variable with its own axioms. These axioms might allow time to be a dense linear ordering without endpoints, or to be even more like the real numbers.

Occasionally the method of temporal arguments uses a special constant symbol, say “n”, to denote now, the present time. This helps with the translation of common temporal propositions (statements, or declarative sentences). For example, let q be “Socrates is sitting down.” The proposition that q has always been true may be translated into first-order temporal logic as

(∀t)[(t < n) → q(t)].

Some temporal logics allow sentences to lack a classical truth-value. The first person to give a clear presentation of the implications of treating declarative sentences as being neither true nor false was the Polish logician Jan Lukasiewicz in 1920. To carry out Aristotle’s suggestion that future contingent sentences do not yet have truth values, he developed a three-valued symbolic logic, with all grammatical declarative sentences having the truth-values of True, False, or else Indeterminate [T, F, or I]. Contingent sentences about the future, such as Aristotle’s prediction that there will be a sea battle tomorrow, are assigned an I. Truth tables for the connectives of propositional logic are redefined to maintain logical consistency and to maximally preserve our intuitions about truth and falsehood. See (Haack, 1974) for more details about this application of three-valued logic.

Different temporal logics have been created depending on whether one wants to model circular time, discrete time, time obeying general relativity, the time of ordinary discourse, and so forth.

12. Supplements

a. Frequently Asked Questions

The following questions are addressed in the Time Supplement article:

  1. What Are Instants and Durations?
  2. What Is an Event?
  3. What Is a Reference Frame?
  4. What Is an Inertial Frame?
  5. What Is Spacetime?
  6. What Is a Minkowski Diagram?
  7. What Are the Metric and the Interval?
  8. Does the Theory of Relativity Imply Time Is Part of Space?
  9. Is Time the Fourth Dimension?
  10. Is There More Than One Kind of Physical Time?
  11. How Is Time Relative to the Observer?
  12. What Are the Relativity and Conventionality of Simultaneity?
  13. What Is the Difference Between the Past and the Absolute Past?
  14. What Is Time Dilation?
  15. How Does Gravity Affect Time?
  16. What Happens to Time Near a Black Hole?
  17. What Is the Solution to the Twin Paradox (Clock Paradox)?
  18. What Is the Solution to Zeno’s Paradoxes?
  19. How Do Time Coordinates Get Assigned to Points of Spacetime?
  20. How Do Dates Get Assigned to Actual Events?
  21. What Is Essential to Being a Clock?
  22. What Does It Mean for a Clock To Be Accurate?
  23. What Is Our Standard Clock?
  24. Why Are Some Standard Clocks Better Than Others?

b. What Science Requires of Time

c. Special Relativity: Proper times, Coordinate systems, and Lorentz Transformations

13. References and Further Reading

  • Callender, Craig, and Ralph Edney. Introducing Time, Totem Books, USA, 2001.
    • A cartoon-style book covering most of the topics in this article in a more elementary way. Each page is two-thirds graphics and one-third text.
  • Callender, Craig. “Is Time an Illusion?”, Scientific American, June, 2010, pp. 58-65.
    • Explains how the belief that time is fundamental may be an illusion because time emerges from a universe that is basically static.
  • Carroll, Sean. From Eternity to Here: The Quest for the Ultimate Theory of Time, Dutton/Penguin Group, New York, 2010.
    • Part Three “Entropy and Time’s Arrow” provides a very clear explanation of the details of the problems involved with time’s arrow. For an interesting answer to the question of whether any interaction between our part of the universe and a part in which the arrow of times goes in reverse, see endnote 137 for p. 164.
  • Damasio, Antonio R. “Remembering When,” Scientific American: Special Edition: A Matter of Time, vol. 287, no. 3, 2002; reprinted in Katzenstein, 2006, pp.34-41.
    • A look at the brain structures involved in how our mind organizes our experiences into the proper temporal order. Includes a discussion of Benjamin Libet’s discovery in the 1970s that the brain events involved in initiating a free choice occur about a third of a second before we are aware of our making the choice.
  • Dainton, Barry. Time and Space, Second Edition, McGill-Queens University Press: Ithaca. 2010.
    • A survey of all the topics in this article, but at a deeper level.
  • Davies, Paul. About Time: Einstein’s Unfinished Revolution, Simon & Schuster, 1995.
    • An easy to read survey of the impact of the theory of relativity on our understanding of time.
  • Davies, Paul. How to Build a Time Machine, Viking Penguin, 2002.
    • A popular exposition of the details behind the possibilities of time travel.
  • Deutsch, David and Michael Lockwood, “The Quantum Physics of Time Travel,” Scientific American, pp. 68-74. March 1994.
    • An investigation of the puzzle of getting information for free by traveling in time.
  • Dowden, Bradley. The Metaphysics of Time: A Dialogue, Rowman & Littlefield Publishers, Inc. 2009.
    • An undergraduate textbook in dialogue form that covers most of the topics discussed in this encyclopedia article.
  • Dummett, Michael. “Is Time a Continuum of Instants?,” Philosophy, 2000, Cambridge University Press, pp. 497-515.
    • A constructivist model of time that challenges the idea that time is composed of durationless instants.
  • Grünbaum, Adolf. “Relativity and the Atomicity of Becoming,” Review of Metaphysics, 1950-51, pp. 143-186.
    • An attack on the notion of time’s flow, and a defense of the treatment of time and space as being continua and of physical processes as being aggregates of point-events. Difficult reading.
  • Haack, Susan. Deviant Logic, Cambridge University Press, 1974.
    • Chapter 4 contains a clear account of Aristotle’s argument (in section 9c of the present article) for truth value gaps, and its development in Lukasiewicz’s three-valued logic.
  • Hawking, Stephen. “The Chronology Protection Hypothesis,” Physical Review. D 46, p. 603, 1992.
    • Reasons for the impossibility of time travel.
  • Hawking, Stephen. A Brief History of Time, Updated and Expanded Tenth Anniversary Edition, Bantam Books, 1996.
    • A leading theoretical physicist provides introductory chapters on space and time, black holes, the origin and fate of the universe, the arrow of time, and time travel. Hawking suggests that perhaps our universe originally had four space dimensions and no time dimension, and time came into existence when one of the space dimensions evolved into a time dimension. He calls this space dimension “imaginary time.”
  • Horwich, Paul. Asymmetries in Time, The MIT Press, 1987.
    • A monograph that relates the central problems of time to other problems in metaphysics, philosophy of science, philosophy of language and philosophy of action.
  • Katzenstein, Larry, ed. Scientific American Special Edition: A Matter of Time, vol. 16, no. 1, 2006.
    • A collection of Scientific American articles about time.
  • Krauss, Lawrence M. and Glenn D. Starkman, “The Fate of Life in the Universe,” Scientific American Special Edition: The Once and Future Cosmos, Dec. 2002, pp. 50-57.
    • Discusses the future of intelligent life and how it might adapt to and survive the expansion of the universe.
  • Lasky, Ronald C. “Time and the Twin Paradox,” in Katzenstein, 2006, pp. 21-23.
    • A short, but careful and authoritative analysis of the twin paradox, with helpful graphs showing how each twin would view his clock and the other twin’s clock during the trip. Because of the spaceship’s changing velocity by turning around, the twin on the spaceship has a shorter world-line than the Earth-based twin and takes less time than the Earth-based twin.
  • Le Poidevin, Robin and Murray MacBeath, The Philosophy of Time, Oxford University Press, 1993.
    • A collection of twelve influential articles on the passage of time, subjective facts, the reality of the future, the unreality of time, time without change, causal theories of time, time travel, causation, empty time, topology, possible worlds, tense and modality, direction and possibility, and thought experiments about time. Difficult reading for undergraduates.
  • Le Poidevin, Robin, Travels in Four Dimensions: The Enigmas of Space and Time, Oxford University Press, 2003.
    • A philosophical introduction to conceptual questions involving space and time. Suitable for use as an undergraduate textbook without presupposing any other course in philosophy. There is a de-emphasis on teaching the scientific theories, and an emphasis on elementary introductions to the relationship of time to change, the implications that different structures for time have for our understanding of causation, difficulties with Zeno’s Paradoxes, whether time passes, the nature of the present, and why time has an arrow. The treatment of time travel says, rather oddly, that time machines “disappear” and that when a “time machine leaves for 2101, it simply does not exist in the intervening times,” as measured from an external reference frame.
  • Lockwood, Michael, The Labyrinth of Time: Introducing the Universe, Oxford University Press, 2005.
    • A philosopher of physics presents the implications of contemporary physics for our understanding of time. Chapter 15, “Schrödinger’s Time-Traveller,” presents the Oxford physicist David Deutsch’s quantum analysis of time travel.
  • Maudlin, Tim. The Metaphysics Within Physics, Oxford University Press, 2007.
    • Chapter 4, “On the Passing of Time,” defends the dynamic theory of time’s flow, and argues that the passage of time is objective.
  • McTaggart, J. M. E. The Nature of Existence, Cambridge University Press, 1927.
    • Chapter 33 restates more clearly the arguments that McTaggart presented in 1908 for his A series and B series and how they should be understood to show that time is unreal. Difficult reading.
  • Mellor, D. H. Real Time II, International Library of Philosophy, 1998.
    • This monograph presents a subjective theory of tenses. Mellor argues that the truth conditions of any tensed sentence can be explained without tensed facts.
  • Norton, John. “Time Really Passes,” Humana.Mente: Journal of Philosophical Studies, 13 April 2010.
    • Argues that “We don’t find passage in our present theories and we would like to preserve the vanity that our physical theories of time have captured all the important facts of time. So we protect our vanity by the stratagem of dismissing passage as an illusion.”
  • Pinker, Steven. The Stuff of Thought: Language as a Window into Human Nature, Penguin Group, 2007.
    • Chapter 4 discusses how the conceptions of space and time are expressed in language in a way very different from that described by either Kant or Newton.
  • Prior, A. N. “Thank Goodness That’s Over,” Philosophy, 34 (1959), p. 17.
    • Argues that a tenseless or B-theory of time fails to account for our relief that painful past events are in the past rather than in the present.
  • Prior, A. N. Past, Present and Future, Oxford University Press, 1967.
    • A pioneering work in temporal logic, the symbolic logic of time, which permits propositions to be true at one time and false at another.
  • Prior, A. N. “The Notion of the Present,” Studium Generale, volume 23, 1970, pp. 245-8.
    • A brief defense of presentism, the view that the past and the future are not real.
  • Savitt, Steven F. (ed.). Time’s Arrows Today: Recent Physical and Philosophical Work on the Direction of Time. Cambridge University Press, 1995.
    • A survey of research in this area, presupposing sophisticated knowledge of mathematics and physics.
  • Sciama, Dennis. “Time ‘Paradoxes’ in Relativity,” in The Nature of Time edited by Raymond Flood and Michael Lockwood, Basil Blackwell, 1986, pp. 6-21.
    • A good account of the twin paradox.
  • Shoemaker, Sydney. “Time without Change,” Journal of Philosophy, 66 (1969), pp. 363-381.
    • A thought experiment designed to show us how time could exist even without any change in the universe.
  • Sklar, Lawrence. Space, Time, and Spacetime, University of California Press, 1976.
    • Chapter III, Section E discusses general relativity and the problem of substantival spacetime, where Sklar argues that Einstein’s theory does not support Mach’s views against Newton’s interpretations of his bucket experiment; that is, Mach’s argument against substantivialism fails.
  • Sorabji, Richard. Matter, Space, & Motion: Theories in Antiquity and Their Sequel. Cornell University Press, 1988.
    • Chapter 10 discusses ancient and contemporary accounts of circular time.
  • Thorne, Kip S. Black Holes and Time Warps: Einstein’s Outrageous Legacy, W. W. Norton & Co., 1994.
    • Chapter 14 is a popular account of how to use a wormhole to create a time machine.
  • Van Fraassen, Bas C. An Introduction to the Philosophy of Time and Space, Columbia University Press, 1985.
    • An advanced undergraduate textbook by an important philosopher of science.
  • Veneziano, Gabriele. “The Myth of the Beginning of Time,” Scientific American, May 2004, pp. 54-65, reprinted in Katzenstein, 2006, pp. 72-81.
    • An account of string theory’s impact on our understanding of time’s origin. Veneziano hypothesizes that our Big Bang event was not the origin of time but simply the outcome of a preexisting state.
  • Whitrow. G. J. The Natural Philosophy of Time, Second Edition, Clarendon Press, 1980.
    • A broad survey of the topic of time and its role in physics, biology, and psychology. Pitched at a higher level than the Davies books.

Author Information

Bradley Dowden
Email: dowden@csus.edu
California State University, Sacramento

Last updated: December 21, 2010 | Originally published: August 11, 2001

Categories: Metaphysics, Philosophy of Science