Can we begin with a short definition of time? Yes, but there are two considerations that must be faced. First, the definition will not be able to to define time in terms of more primitive, yet familiar, notions. Second, succinct definitions of time are rarely helpful unless they are backed up with a more elaborate and systematic treatment of time. The brief definitions that stand alone are either trivial (Time is the collection of instants) or too imprecise (Time is the dimension of causality) or circular (Time is what keeps everything from happening all at once) or simply cryptic (Time is the flow of events past the stationary I). When philosophers ask,'' what is time'', they normally are asking for a philosophical theory designed to answer many of the philosophical questions about time such as whether the past-present-future distinction is objective and how we should understand the flow of time. A succinct definition of time will be adequate only insofar as it is backed up by this more elaborate theory.

Consider what a more systematic theory of time should do. It should reveal, among other things, the relationship between time and mind. It is easy to confuse time itself and the perception of time. Does time exist for beings that have no minds?

A theory of time should reveal what physical science presupposes and implies about time. Does it imply the possibility of time travel , for instance? What does it assume about the relationship between time and space time? Physicists say that, locally, time is made of a linear continuum of instants, with each instant lasting for zero seconds. Being a continuum implies that between any two instants there is another instant. No time measurement is so fine grained that it could detect whether this is true for instants that are extremely close together in time. If so, then on what grounds do scientists know that time is a continuum?

A philosophical theory of time should describe the relationship between instants and events. Does the instant that we label as "11:01 AM" 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 raises the thorny metaphysical issue of absolute vs. relationel theories of time.

A theory of time should address the question of time's apparent direction. If the projectionist in the movie theater shows a film of cream being added into black coffee but runs the film backwards, we in the audience can immediately tell that events couldn't have occurred this way. We recognize the arrow of time because we know about the one-directional processes in nature--that brown coffee never unmixes into black coffee and cream, for example. This arrow becomes less and less apparent to the viewer as the film subject gets smaller and smaller and the time interval gets shorter and shorter. Philosophers disagree about the explanation of this arrow. The arrow appears to be very basic for understanding nature, yet it is odd that asymmetries in time don't appear in most of the basic dynamical laws of physics. Philosophers also wonder what life would be like in some far off corner of the universe if the arrow of time were reversed there. Would our counterparts walk backwards up steps while remembering the future?

Another philosophical problem about time concerns the questions, "What is the present moment and why does it move into the past?" Present events seem to flow by, receding ever farther into the past. Many philosophers are suspicious of this notion of the flow of time. They doubt whether it is a property of time as opposed to being some feature of human perception. There are also suspicions about the present, the feature that is referred to by the indexical word 'now.' If the present is real, then why isn't there a term for it in the laws of science?

For a last example of a philosophical problem regarding time, some philosophers argue that the future is not real, but the present is. These philosophers have a problem with the apparent implication that, if the future were real, then it would be fixed now, and we would not have the freedom to affect that future. Other philosophers disagree.

A full theory of time should address this constellation of philosophical issues and paradoxes about time.               How is time related to mind?                          Kant,believed our sense of time is a necessary condition of our experience. Mach believed our sense of time is a simple sensation. Most researchers today would reject both these positions and claim that our sense of time is indirectly related to our ability to sense all sorts of changes; our sense of time is an intellectual construction that helps us account for our experience.

Does this time, which is sensed, exist objectively? It can be very difficult to distinguish a genuine objective aspect of reality from an appearance of reality or from the particular perspective from which we regard that reality. This difficulty arises when we ask: If consciousness were absent, would time be absent, too? Consciousness probably requires a brain-based sense of time, but does time require consciousness?

This metaphysical question has been much discussed. Aristotle raised the question: "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 some one to count there cannot be anything that can be counted..." [223a] He doesn't 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 movement's being numbered were consciousness to exist. Aristotle's distinction foreshadows the modern distinction between psychological time and physical time.

Physical time is public time. Psychological time is private time. We are referring to psychological time when we say that time passes slowly for someone who is waiting anxiously for the water to boil on the stove. We are referring to physical time when we speak of the time that a clock measures. When a physicist defines speed to be the rate of change of position with respect to time, the term 'time' refers to physical time. Psychological time is best understood as being consciousness of physical time. Psychological time stops when consciousness does, but physical time does not. Physical time is more basic for helping us understand our shared experiences in the world. It is more useful than psychological time for doing science.                                   St Augustine said time is nothing in reality but exists only in the mind's apprehension of that reality. Henry of Ghent and Giles of Rome both said time exists in reality as a mind-independent continuum, but is distinguished into earlier and later parts only by the mind. 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. In the 13th century, Duns Scotus 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 structures our perceptions so that we know a priori that time is like a mathematical line. Time is, on this theory, a form of conscious experience.

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.

The philosophical issue of the flow of time concerns whether this flow is an objective feature of reality or, instead, is entirely a feature of human perception.

Finally, the question about the relationship between time and the observer's frame of reference is not a question about the relationship about time and mind, the question of whether time requires consciousness.

A wide variety of short answers have been given to the question "What is time?" Some of these are backed up by more elaborate theories of time, and some are not. Plato, for example, said time is the circular motion of the heavens. Aristotle said it's not motion but the measure of motion. Kant, taking a very different approach to time, said it is a form that the mind projects upon the external things-in-themselves. A more modern definition says time is the dimension of causality.                                                          Aristotle   provides an early, careful answer to the question "What is time?" when he says time is the "number of movement in respect of the before and after, and is continuous.... In respect of size there is no minimum; for every line is divided ad infinitum. Hence it is so with time." [Physics, 220a] Occasionally Aristotle speaks as if time were motion, but in these passages, he also asserts that time, though linked to motion, is neither the circular motion of the heavens (Plato's view) nor any other motion. He believes time is something by which we measure motion.

In the 17th century, the English physicist Isaac Barrow rejected Aristotle's linkage between time and change, or between instants and events, by saying that time is something which exists independently of motion and which existed even before God's creation. Barrow's student, Isaac Newton, agreed. Newton argued very specifically that time and space are an infinitely large container for all events, and the container exists with or without the events. Space and time are not material substances, but are like substances, he added, in not being dependent on matter or motions or anything else except God.

Gottfried Leibniz objected. He argued that time is not an entity existing independently of events. Leibniz insisted that Aristotle and Newton, despite their differences, had overemphasized the relationship between time and duration while underemphasizing the fact that time ultimately involves order as well. Time is an ordering of changes, says Leibniz, the overall ordering of all non-simultaneous events. This is why time 'needs' events, so to speak. Leibniz added that this order is also a "something" as Newton had been insisting, but it is an ideal entity. Triangles, numbers, and relations are also ideal entities.

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 infinite 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's 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 apriori truths began to lose favor.

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 couldn't have caused A. This was the first causal theory of time. Its usefulness depends on a clarification of the notorious notions of causality and possibility without giving 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'. That is, 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 tossing a rock into a still pond? Imagine what the initial conditions at the edge of a pond must be like to produce correlated, incoming, concentric water waves that would expel the rock and leave the water surface smooth.] 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, a temporally symmetric notion. For Hume, there is nothing metaphysically deep about causes preceding their effects; it's 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.

One way to answer the question "What is physical time?" is to declare that it is whatever the time variable t is denoting in the best-confirmed and most fundamental theories of current science. Many philosophers complain that this answer is incomplete because, although a philosophical theory of time should be informed by what science requires of time, the philosophical theory should progress beyond current physical theory.

Is time like a line or, instead, like a circle? Perhaps this question should not be answered by definition, although it sometimes has been. The concept of linear time first appeared in the writings of the Hebrews and the Zoroastrian Iranians. The Roman writer Seneca advocated linear time, but most of the ancient Greeks and Romans believed time to be ultimately cyclic. Aristotle gave psychological reasons for why the circle is an appropriate model. His point was that we cannot conceive of a first time; for any first time we could conceive of a time before that. Neither Aristotle nor Plato envisioned their cosmic cyclicity as requiring any detailed endless repetition such as the multiple births of Socrates, though some Stoic philosophers did adopt this drastic position. Rejecting circularity, Islamic and Christian theologians adopted the Jewish notion that time is linear with the universe being created at a definite moment in the past. Augustine explicitly objected to Aristotle's belief that time is circular, insisting 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. It was not until 1602 that the concept of linear time was clearly and explicitly formulated--by the English philosopher Francis Bacon. In 1687, Newton captured some of this viewpoint when he represented time mathematically by using a line rather than a circle. 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, and it remains so today.

Quantum field theory and Einstein's general theory of relativity are the most fundamental theories of physics. According to both these theories, spacetime is a collection of points called "spacetime locations" where physical events occur. Spacetime is four dimensional and a continuum, with physical time being a distinguished, one-dimensional sub-space of this continuum.

In 1908, the mathematician Hermann Minkovski had an original idea in metaphysics regarding space and time. He was the first person to realize that spacetime is more fundamental than time or than space. As he put it, "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." The metaphysical assumption behind Minkowski's remark is that what is 'independently real' is what does not vary from one reference frame to another. It's their "union," what we now call "spacetime," that doesn't vary. It follows that the division of events into the past ones, the present ones, and the future ones is also not 'independently real'.

Newton would have disagreed. He declared that every observer can in principle determine time intervals that depend in no way on the observer's frame of reference. If the time interval between two lightning flashes is 100 seconds on someone's clock, then the interval also is 100 seconds on your clock, even if you are flying by at an incredible speed. Albert Einstein rejected this piece of common sense in his 1905 special theory of relativity when he declared that the time interval (and the distance) between two events depends on the observer's reference frame. As Einstein expressed it, "Every reference body has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event." Each reference frame (or reference-body) divides spacetime differently into its time part and its space part. This feature of our universe is what Einstein calls the "relativity of simultaneity." It is a relativity for distant events only, not for events happening at the same place.

Science assigns numbers to times because, in any reference frame, the happens-before order-relation on events is faithfully reflected in the less-than order relation on the time numbers (dates) that we assign to events. In the fundamental theories such as relativity and quantum mechanics, the values of the time variable t are real numbers, not merely rational numbers, with each number designating an instant of time. Time is a linear continuum of instants, similar to the mathematician's line segment. Therefore, if these fundamental theories are correct, physical time is one-dimensional rather than two-dimensional, and continuous rather than discrete. One can't be sure from this that time is linear rather than circular because a segment of a circle is also a linear continuum. If time were circular, then Homer might write his Iliad and Odyssey epics in the future, a possibility that appealed to the ancient Stoic philosophers. The logic of the term 'time' doesn't rule out a nonlinear structure, but there is no reason to believe it occurs.   Relativity implies nothing about the universe's topology.

Regarding the instants, time's being a linear continuum implies there is a nondenumerable infinity of them. It also implies they are so densely packed that between any two there is a third, and yet no instant has a next instant. There is little doubt that the actual temporal structure of events can be embedded in the real numbers, but how about the converse? That is, to what extent is it known that the real numbers can be adequately embedded into the structure of the instants? The problem is that, although time is not quantized in quantum theory, for times shorter than about 10 to the minus 43 seconds, the so-called Planck time, science has no experimental grounds for the claim that between any two events there is a third. Instead, the justification is that the assumption of continuity is convenient and useful, and that there are no better theories available.

Because of quantum mechanical considerations, physicists agree that the general theory of relativity must fail for durations shorter than the Planck time, but they don't know just how it fails. Most importantly here, there is no agreement among physicists as to whether the continuum feature of time will be adopted in the future theory of quantum gravity that will be created to take account of both gravitational and quantum phenomena. The string theory of quantum gravity predicts that time is continuous, but the main alternative to string theory, loop quantum gravity, does not. If loop quantum gravity becomes the accepted way of unifying quantum mechanics and relativity, then philosophers of science will not conclude that ordinary physical time does not exist. Rather, they will conclude that time is itself constituted by something nontemporal.

In 1922, the Russian physicist Alexander Friedmann predicted from general relativity that the universe should be expanding. In 1929, the American astronomer Edwin Hubble made careful observations of clusters of galaxies and confirmed that the universe is undergoing a universal expansion. Each galaxy cluster is moving away from most every other. So, at any earlier moment the universe was more compact. Projecting to earlier and earlier times, and assuming that gravitation is the main force at work, the astronomers now conclude that 13.7 billion years ago (plus or minus 1%) the universe was in a state of zero size and infinite density. Because all substances cool when they expand, physicists believe the universe itself must have been cooling down over the last 13.7 billion years. Therefore, the universe started out very hot and very small. The big bang theory is a theory of how our universe evolved, how it expanded and cooled from its beginning process.  This beginning process is called the "big bang." As far as we know, the entire universe was created in the big bang, and time itself came into existence 'at that time'.

In the literature in both physics and philosophy, descriptions of the big bang often assume that a first event is also a first instant of time and that spacetime did not exist outside the big bang. This intimate linking of a first event with a first time is a philosophical move, not something demanded by the science. It is not even clear that it's correct to call the big bang an event. The big bang event is a singularity without space coordinates, but events normally must have space coordinates. One response to this problem is to alter the definition of 'event' to allow the big bang to be an event. Another response, from James Hartle and Stephen Hawking, is to consider the past cosmic time-interval to be open or unbounded at t=0 rather than closed or bounded by t=0. Looking back to the big bang is then like following the positive real numbers back to ever smaller numbers without ever reaching a smallest positive one. If Hartle and Hawking are correct that time is actually like this, then the universe had no beginning event, but it has a finite amount of past time, and the term 'the big bang' refers not to any single event. But in order to simplify the discussion ahead, this article will speak of 'the' big bang event as if it were a single event.

There are serious difficulties in defending the big bang theory's implications about the universe's beginning. They are based on the assumption that the universal expansion of clusters of galaxies can be projected all the way back. Yet physicists agree that the projection must fail in the Planck era, that is, for all times less than 10 to the minus 43 seconds after 'the' big bang. Therefore, current science cannot speak with confidence about the nature of time in the Planck era, nor whether time existed before that era. If a theory of quantum gravity does get confirmed, it should provide information about the Planck era, and it may even allow physicists to answer the question, "What caused the big bang?" However, at present, the best answer is probably "Nothing; it just happened." The philosophically radical, but theologically popular, answer, "God caused the big bang, but He, himself, does not exist in time" is cryptic because it is not based on a well-justified and detailed theory of who God is, how He caused the big bang, and how He can exist but not be in time. It is also difficult to understand St. Augustine's remark that "time itself was made by God." On the other hand, for a person of faith, belief in God as creator is usually stronger than belief in any scientific hypothesis or in any epistemological desire for a scientific justification of the remark about God or in the importance of satisfying any philosopher's demand for clarification.  The big bang theory is accepted by the vast majority of astronomers, but it is not as firmly accepted as is the theory of relativity.

Relativity theory challenges a great many of our intuitive beliefs about time. The theory is inconsistent with the common belief that the order in which two events occur is independent of the observer's point of view. For events occurring at the same place, relativity theory implies the order is absolute (independent of the frame), but for distant events occurring close enough in time to be in each other's absolute elsewhere, event A can occur before event B in one reference frame, but after B in another frame, and simultaneous with B in yet another frame.

Science impacts our understanding of time in many other fundamental ways. Relativity theory implies there is tme dilation between one frame and another. For example, the faster a clock moves, the slower it runs, relative to stationary clocks. Time dilation shows itself when a speeding twin returns to find that his (or her) earth-bound twin has aged more rapidly. This surprising dilation result has caused some philosophers to question the consistency of relativity theory, arguing that, if motion is relative, then from the perspective of the speeding twin, he should be the one who aged more rapidly. This argument is called the twins paradox . Experts now are agreed that the mistake is within the argument for the paradox, not within relativity theory. The argument fails to notice the radically different relationships that each twin has to the rest of the universe as a whole.

There are two kinds of time dilation. Special relativity's time dilation involves speed; general relativity's involves acceleration and gravitational fields. Two ideally synchronized clocks need not stay in synchrony if they undergo different accelerations or different gravitational forces. This effect would be especially apparent if one of the two clocks were to fall into a black hole . A black hole can form when a star exhausts its nuclear fuel and contracts so compactly that the gravitational force prevents anything from escaping the hole, even light itself. The envelope of no return surrounding the black hole is its event horizon. As a clock falls toward a black hole, time slows on approach to the event horizon, and it completely stops at the horizon (not just at the center of the hole)--relative to time on a clock that remains safely back on earth.

The supplement  to this article continues with the topic of what science requires of time, and it provides background information about other topics discussed in this article.

Let's begin by discussing activities that have been taken to be time travel but aren't under serious consideration by philosophers today. (a) Remembering an earlier event in your life may be a kind of mental time travel, although there's a difference between experiencing an event and remembering it. Because it's at best travel only in psychological time rather than physical time, philosophers haven't shown much interest in this sort of time travel. (b) If you get on a plane on the earth's surface and travel west, you will cross a time zone and instantly go back an hour. All you've really done though is changed your reference frame, so this is a trivial form of time travel. (c) If your body were quick-frozen in the year 2,000 and thawed in 2,088, then you would have traveled forward 88 years in clock time but only a few seconds of your biological time. This is a case of biological time travel, not a case of physical time travel and so has not been of interest to philosophers. (d) A change in the direction of the arrow of time isn't considered to be a case of time travel.

Travel to the future

Time travel can be to the past or the future. Because travel to the future is easier and more practical, it will be discussed first. There are two straightforward ways to travel into another person's future. In the twins paradox , a person speeding away from his twin who remains on earth will, upon reunion, have entered the earth-twin's future. Second, according to general relativity, if the twin goes to a stronger gravitational field by leaving the dinner table and descending to the cellar for a bottle of wine and then returns, he will have entered the future of his twin who stayed at the dinner table. When someone enters a relatively stronger gravitational field, their time slows down relative to the time of those who don't enter the stronger field.

Regarding the first kind of time travel to the future, if you have a fast enough spaceship, you can travel to the year 4,500 A.D. and see the future of earth. You can affect that future, not just see it. This is a direct consequence of the time dilation described in the theory of relativity. You can travel to someone else's future, not your own. You're always in your own present. Unfortunately, once you go to 4,500 A.D. (as judged in a frame of reference in which the earth is considered stationary), you are stuck in the earth's future. You can not reverse course in your spaceship and return to the 21st century on earth. You must live with the consequence that all your friends have died centuries ago. Visits to the future are permanent, not temporary.

On this trip to 4,500 A.D., how much time would elapse on your own clock? The answer depends on how fast your spaceship goes, what accelerations occur, and whether gravitational forces are acting. The faster your spaceship goes, the less time it will take--actually take, not just appear to take. As you approach infinitesimally close to the speed of light, the trip to 4,500 A.D. will take essentially no time at all. That's from your own perspective though; observers who remained stationary on earth and judged your flight from that perspective will have observed your speedy travel for thousands of years.

In science fiction movies, which almost always depict nonrelativistic time travel, time travelers suddenly appear from out of the past, and other travelers suddenly disappear from now and pop into the future. These phenomena have never been observed, despite the parapsychological literature. If they were reliably observed, then we would consider the hypothesis that spacetime has an extra dimension allowing time travel. The discontinuous worldline in ordinary 4-d spacetime could actually be a continuous trajectory in 5-d spacetime. One would wonder, though, how anyone could ever verify (check) that the time traveler took one trajectory in the higher dimension rather than another.

Travel to the past

One of the major metaphysical assumptions made in the analysis of time travel to the past is that the world is never logically contradictory. This is the heart of the Grandfather Paradox. According to this paradox, you step into a time machine, go back and kill your grandfather before he's met your grandmother, so you prevent your own birth. Therefore, you both exist and don't exist right now. This result violates the law of noncontradiction, so we may conclude that we erred in assuming the possibility of this sort of time travel. If time travel is going to exist, it can't permit any change in what is known to have happened--presuming that logic is more fundamental than metaphysics. More generally, John Earman proposed that we grant law-status to consistency constraints on all spacetimes with closed timelike curves.

How about influencing history instead of changing it? The time traveler helps make history what it was. For example, Joe Stalin, the dictator of Russia, was 21 years old in 1900. Let's suppose time machines are invented in 2030. In that year, Sam decides to assume the identity of Stalin. He knows Russian history, speaks fluent Russian, is 21 years old, and looks like Joe Stalin did at 21. Sam enters the newly invented time machine, goes back to 1900, secretly murders Stalin, then starts calling himself "Stalin". Sam never reveals his past [as Sam], and he eventually becomes the dictator of Russia.

This possibility requires altering our normal assumptions about personal identity. Because Stalin really died in 1953, Sam must die in 1953, many years before he is born. To accept that the time travel occurred, we'd have to revise our current notion of personal identity as well as our notion of what can be remembered, assuming that Sam-Stalin remembers life before stepping into his time machine.

Sam's world line will be composed of discontinuous segments. The world lines of more continuous time travelers might be a loop, a closed timelike curve. Either possibility implies backward causation. Some philosophers believe backward causation can be ruled out by the definition of 'cause,' just as they can rule out Monday ever immediately following Friday. Many other philosophers disagree on the grounds that backward causation is improbable or nonexistent, but not impossible. 

Another implication of Sam's time travel is his apparent violation of the law of conservation of matter by popping into existence in 1900. Must we also revise that law? The modern version of the law of conservation of matter-energy is that the conservation is statistical; matter is conserved on average. The shorter the time span and the smaller the mass involved then the more likely that there can be violations in conservation.

There are other significant implications involved with this sort of participatory time traveling--traveling back in time to participate in what actually happened. The future is oddly constrained by the time traveling. After Stalin's death, the world's events must allow Sam at age 21 to enter the time machine. Nothing can happen to prevent Sam getting to the machine. All his enemies somehow must botch their attempts to kill him. Attempted sabotage of the time machine must also fail. Scientists viewing these attempts will be surprised that they are continually yet inexplicably frustrated by unfavorable circumstances. Looking back from the year 2030 it will appear as if the world conspired to ensure that a predestined event occurred. It has been argued that because we've never seen the world conspire with massive coincidences, this sort of time travel never occurs even if it is logically and conceptually possible.

An additional argument against time travel of the kind that influences past events but doesn't change them is that by now we should have seen all sorts of time traveler tourists from the distant future. Nobody has ever seen one, despite some unreliable witnesses described in supermarket tabloids. Therefore, time travel most probably never occurs even if it could. The principal counter is that there might be very good reasons why our time hasn't yet been visited. The travelers might be uninterested in us. It might be very expensive to go to our time. They might be here but be invisibly cloaked so as not to interfere with us. Therefore, it is jumping to conclusions to be so pessimistic about the probability of time travel.

Admittedly, though, no one has any practical and realistic plans for how to build a time machine. The best plans use such phrases as "First, take a worm hole and...." Kurt Godel was the first person other than Einstein to have realized that the general theory of relativity does permit a physical object to travel at less than the speed of light and yet arrive at its own past. This travel requires the warping of spacetime itself, tipping the light cone of the traveling object. The time line dips back into the past and could form a closed curve in spacetime. Since Godel's initial work in 1949, mathematicians and theoretical physicists have described other time machines, or at least universes containing backward time travel, that are consistent with Einstein's equations of general relativity. Stephen Hawking believes all these time machines are ruled out by the laws of general relativity. General relativity theory is so complex that it isn't always clear, even to the experts, what is and isn't allowed by the theory.  Other physicists accept that Einstein's equations do allow time travel, but they rule out these solutions as being physically impossible or improbable for other reasons, such as those mentioned above.

Probing the possibility of a contradiction in backwards time travel, John Earman has described a rocket ship that carries a very special time machine. The time machine is capable of firing a probe into the 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' of the probe is detected by a sensing device on the ship. Does the probe get launched? The way out of Earman's paradox seems to require us to accept that (a) the universe conspires to keep people from building the probe or the safety switch or the sensing device, or (b) time travel probes must go so far back in time that they never make it back to the time when they were launched, or (c) past time travel is impossible. 

Feynman diagrams in particle physics were described by Feynman himself as illustrating how a particle's moving forward in time is actually its antiparticle moving backward in time. However, physicists don't take Feynman's suggestion literally. As a leading particle theorist, Chris Quigg of Fermi National Accelerator Laboratory, explained, "It's not that antiparticles in my laboratory are actually moving backward in time. What's really meant by that is that if I think of a particle moving from one place to another forward in time, the physical process is the same as it would be if we imagine running the film backward and also changing the particle into an antiparticle."

In addition to time travel that changes the past and time travel that participates in the past, consider a third kind, time travel that reaches the past of a different universe. This idea appeals to an unusual interpretation of quantum mechanics, the parallel universes interpretation. According to this interpretation, everything that can happen does happen in some universe or other. There's a universe in which the Nazis won World War II and Stalin was assassinated. There's another universe in which the Nazis won World War II and Stalin escaped all assassination attempts. On this theory of time travel, for you to travel back in time and have lunch with President Abraham Lincoln is for you to stop existing in the present universe as you enter the time machine and for you to appear earlier in time in a parallel universe, one in which you in fact did have lunch with Abraham Lincoln. The theory implies that we must change our current view of what makes a person the same person through time [say, bodily identity and continuity of consciousness through time in a single universe] and accept some kind of trans-universe identity.

When you set your alarm clock for 7:00, does the time of 7:00 cause your alarm to go off? No, although it wouldn't go off if it weren't 7:00, under the circumstances. Such is the nature of causality. It is generally agreed that time causes nothing.

Another question, underlying the point about your alarm clock, is whether 7:00 exists despite what happens. Absolute and relational theories of spacetime offer opposing answers to the question.

Absolute theories say time exists independently of the spacetime relations exhibited by physical events. Relational theories say it does not. Some absolute theories describe spacetime as being like a container for events. The container exists with or without events in it.

The term 'absolute' in this context does not mean independent of the observer, but independent of the events. The absolute theories imply that spacetime could exist even if there were no physical objects and events in the universe, but relational theories imply that spacetime is nothing but objects, their events, and the spatiotemporal relationships among them, though as we shall discuss in a moment, much depends on whether spacetime also involves possible events in addition to actual events. Everyone agrees time cannot be measured without there being objects and changes, but the present issue is whether it exists without objects and changes.

Aristotle took a position regarding the relationship between time and change when he remarked that, "neither does time exist without change [218b]." However, the battle lines were most clearly drawn in the 17th century when Leibniz explicitly said there is no time without actual change, Newton protested that time exists regardless of whether anything changes, and both persons offered several arguments for their positions.

 Leibniz's principal argument says there is no difference between the presence and absence of absolute space. If there were such a difference, then God could have made everything be five miles east of where it is and have had all the universe's events occur five minutes later. But that's absurd; there's no way to detect such a difference. So, by the Principle of the Identity of Indiscernibles, the two different universes would actually be one.

Newton's two-part response: (1) The bucket thought-experiment shows that acceleration relative to absolute space is detectable [by looking for the presence centrifugal forces]; thus absolute space is real. (2) Besides, there don't have to be discernible differences for humans; God might have had a sufficient reason for creating the world at a given place and time even though mere mortals cannot comprehend His reasons. Leibniz is correct, says Newton, to accept the Principle of Sufficient Reason and the Principle of the Identity of Indiscernibles, but Leibniz is mistaken in using these to argue against absolute space.

Huygens, Berkeley , and Mach 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. However, some philosophers say Reichenbach and the early Einstein may have been overstating the amount of metaphysics that can be extracted from the physics. Newton's own absolute theory of space used the notion of a space-filling material aether at rest in absolute space with distances and times being independent of reference frames, and this is admittedly inconsistent with special relativity, but other absolute theories are consistent with current science.

Absolute theories were dominant in the 18th and 19th centuries, and the relational theories were dominant in most of the 20th century, but at the end of the century, absolute theories gained some ground and there is no convergence of opinion on this prominent issue.

Absolute theories are called 'substantival' or 'substantial' if they require spacetime to be a substance. These are the kind of absolute theories discussed here. Absolutists disagree among themselves about what it means to be a substance. It does not mean that spacetime is a kind of stuff out of which physical events are composed. Absolutists have described spacetime as "an antecedent arena for events" and "ontologically prior to events" and "an irreducible object of predication" and "the substrata for properties" and "the domain of the intended models of the basic physical theories." The container metaphor may work for special relativity, but general relativity requires that the curvature of spacetime be affected by the distribution of matter, so today it is no longer plausible for an absolutist to assert that the 'container' is independent of what it contains.

What is implied by saying time is a relationship among events? For example, if events occur in a room a second before and after 11:01 AM, but not at that instant, must the relationist say there never was a time of 11:01 AM in the room? One relationist response is to say 11:01 exists because somewhere something is happening then. There can be no 'empty' time, the relationist says. Will this relationist strategy for time work also for space? Can there be no empty space? No merely possible places? That is a bigger philosophical problem. For elegant science, we need to speak of an electron's taking a different path from the one it actually took. Is there a coherent role for these paths of nonexistent events in the relationist's 'relationships among events'?

If the relational theory were to consider spacetime points to be permanent possibilities of the location of events, then the relationist theory would collapse into substantivalism, and there would no longer be a difference between the two theories, John Earman has argued. To the absolutist, a spacetime point is also just a place where something could happen. Lawrence Sklar says that if relationists are going to talk about locations between material objects where no objects exist, then they "had better allow talk about possible objects and their possible spatial relations" because "versions of relationism that eschew such notions are pretty implausible...." The same point applies to possible events.

Hartry Field argues for the absolute theory by pointing out that modern physics requires gravitational and electromagnetic fields that cover spacetime. They are states of spacetime. These fields cannot be states of some Newtonian aether, but there must be something to have the field properties. What else except substantive spacetime points?

"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 Plato. Santayana offered another metaphor: "The essence of nowness runs like fire along the fuse of time." It is universally agreed that time doesn't flow along at a rate of one second per second, so the philosopher's goal is to clarify the metaphor of time's flow.

There have been three major 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. The second is that it is not an illusion but rather is subjective, being deeply ingrained due to the nature of our minds. The third is that it is objective, a feature of the mind-independent reality that has so far been missed by today's scientific laws.

Some philosophers have argued that the passage of time is a feature of the world to be explained by noting how events change. An event such as the death of Queen Anne can change from having the property of being future, to having the property of being present, to having the property of being past (to one of her contemporaries). Agreeing that events can change their properties in this manner, J. M. E. McTaggart argued that the concept of time itself is absurd because it is contradictory for Queen Anne's death to be both present and past. Many other philosophers believe events do not change any of their 'essential' properties. An event's 'changing' from being future to being present to being past is not a real change in its essential properties, but only in its relationship to the observer. So, it is concluded by these philosophers that the notion of time's flow is a myth.

Ludwig Wittgenstein approached the question of why the flowing conception of time is such a compelling myth by asking us to be more attentive to the proper use of our words--and quit considering time to be a queer medium:

In our failure to understand the use of a word, we take it as the expression of a queer process. (As we think of time as a queer medium, of the mind as a queer kind of being.)

Most physicists do not believe time flows from future into past. Instead they accept the idea that events merely exist in spacetime. This idea is called the ‘block universe' idea. The term was coined by William James. Advocates of the block universe commonly argue that the notion of time's flow is simply a mistake or else that it is a subjective feature of psychological time to be explained, say, by a person's having more memories and more information at later times. They argue that the only sense that can be made of the metaphor "Time flows" is that time exists.

Other physicists and philosophers, however, do not consider time's flow to be a myth and have not been satisfied with these analyses. 

What gives time its direction or 'arrow'? Actually, time is directional in two senses. In one sense, which is not the sense meant by the phrase "the arrow of time", time is directed from the future to the past. This is the sense in which any future event is temporally after any past event. Because this is implied by the very definition of the terms 'future' and 'past,' to say "Time is directed from future to past" is to express a merely conventional truth of little interest to the philosophical community.

However, time is directed in a second sense, one that isn't merely a matter of the definition of the relevant terms. This is time's arrow. It's about the particular ordering of events in time. It is what distinguishes events ordered by the happens-before relation from those ordered by its converse, the happens-after relation. It is still an open question in philosophy and science as to what it is about events that gives them an arrow.

This arrow is evident in the fact that footprints in the sand are traces of the past, never traces of the future. This arrow is also evident in certain processes, such as the process of mixing cool cream into hot coffee. You soon get lukewarm, brown coffee, but you never notice the reverse--lukewarm coffee unmixing into a cool part and a hot part. Such is the way this irreversible thermodynamic process goes. The arrow of an irreversible physical process is the way it normally goes, the way it normally unfolds through time--if not through all time, then through time in the present epoch of the universe's history. The amalgamation of the universe's irreversible processes [and of the temporally asymmetric features such as the footprints in the sand being traces of past events, not future events] produces the cosmic arrow of time, the master arrow. Usually this arrow is what is meant when one speaks simply of "time's arrow."

The goals of a theory of time's arrow are to understand why this arrow exists, what it would be like for the arrow to reverse direction, and what the relationships are among the various more specific arrows of time--the various temporal asymmetric processes such as entropy increases [the thermodynamic arrow], causes preceding their effects [the causal arrow], the universe's spatial expansion, our knowing the past more easily than the future, and so forth.

If physical processes in time do have an arrow, and if the processes obey scientific laws, and if these laws are to be accounted for by the basic laws of physics (the laws governing the microscopic constituents of matter), then you might think that an inspection of these basic laws would readily reveal time's arrow. It won't. Except for the fact that it takes more than a trillion times longer for a kaon to decay into pions than for a kaon to be produced by motion reversal [which is essentially time reversal] from the pions, all the basic laws are time symmetric. This means that if a certain process is allowed by the equations, then that process reversed in time is also allowed. In other words, the basic laws of science are insensitive to the distinction between past and future.

To illustrate, let's suppose you could have a movie of a basic physical process such as two atoms bouncing off each other. You can't have such a movie because the phenomenon is too small, but let's forget that fine point for a moment. If you had such a movie, you could run it forwards or backwards and both showings would illustrate a possible process according to the laws of science. Time's arrow isn't revealed in this microscopic process. The reason why this result is so interesting to scientists and philosophers is that, if you had a movie of the mixing of hot, black coffee and cool cream, then you could tell which way is the right way to show the movie. The arrow of time that was absent in the microscopic movie would be evident in the macroscopic movie. This difference between microscopic movies and macroscopic movies is odd because ordinary processes are supposed to be composed of more basic processes. Why does the arrow of time appear in one movie but not the other?

Ludwig Boltzmann had an answer. He was the first to attempt to show how an irreversible macroscopic phenomenon may arise from reversible microscopic laws. He showed that macroscopic thermodynamic processes such as heat in a gas are irreversible because the probability of their actually reversing is insignificant. There are more lukewarm microstates of the set of its constituent molecules than there are microstates with separated hot and cold regions, so the system evolves in the 'direction' of what is most probable. To express the point somewhat more precisely, let A be the set of microstates of an isolated container in which one part of the container contains hot gas and a separate part contains cold gas. Let B be the lukewarm microstates. Assume all the microstates are equally probable apriori. The number of B states is dramatically larger than the number of A states, so the probability that one of the A states will soon lead to one of the B states is almost one whereas the probability that a B state will soon lead to an A state is almost zero. That is why the process of heat in a gas is irreversible.

The law of physics describing heat processes is the second law of thermodynamics, an irreversible law that says a change occurring in an isolated, macroscopic system will most probably not lead it into a state of lower entropy. Entropy is approximately a measure of a system's disorder, so an entropy increase is a trend toward decay, running down, rusting, the conversion of useful energy into heat. Isolated systems change toward disorder because disorder is so probable, Boltzmann would say. So, entropy's relentless increase accounts for the irreversibility of thermodynamic processes, and this is the basis of time's arrow, according to Boltzmann.

A dynamic system is a system defined by the values of the positions and velocities of all the system's particles--such as the places and speeds of the atoms in a cup of coffee) Henri Poincare's recurrence theorem in statistical mechanics says every isolated dynamical system will eventually return to a state as close to the initial state as we might wish. Wait long enough, and the lukewarm brown coffee will separate into hot black coffee and cool white cream. In other words, strictly speaking, there are no irreversible processes. So, there is a contradiction between Poincare's theorem and Boltzmann's proof. The second law implies that entropy increases, but Poincare's theorem implies that entropy remains the same over the long haul. The resolution of the problem is to revise the second law: it's probable, for period of time short compared to the Poincare period, that the higher entropy state is the later entropy state.

If the thermodynamic arrow of time [for periods much shorter than Poincare's recurrence time] is to be explained by entropy increase, as Boltzmann hoped, then we want to know why entropy was so low in the past. You wouldn't expect it to be low in the past if you started from the present and applied the basic time symmetric laws of science. That is, hasn't Boltzmann really shown only that entropy change is associated with entropy increase, so that entropy change toward the past implies high entropy in the past? And Boltzmann has failed to show why entropy in our past was so low. These criticisms come from Boltzmann's colleague in Vienna, Franz Loschmidt. Boltzmann's response used the anthropic principle. He said we are the kind of creatures whose physiology is such that we are "bound to regard the future as being the direction in which entropy increases", so THAT explains why entropy increases toward the future, but not the past.

Loschmidt took a different view. He said the observed occurrence of only entropy-increasing processes in the present era of history must be a consequence of the particular initial conditions in our region of the universe and not a consequence of the laws governing molecular motions, nor a consequence of some anthropic principle. Boltzmann didn't realize that the temporal asymmetry he got out of a system if just the asymmetry he put in. Agreeing with Loschmidt, Einstein argued that the asymmetry we see when a wave expands from its source but never converges coherently to a point is just as statistically based as Boltzmann's entropy flow; and both asymmetries rest on what the initial conditions happen to be like.

If so, then entropy increase is not the deep reason behind time's arrow. Instead, the arrow of time depends essentially on the universe's having started with the initial configuration that it had. This analysis leads naturally to the request for an explanation of the initial configuration of our universe, an explanation we would hope to get from cosmologists.

Our original question was: Why does the arrow of time appear in the coffee movie but not in the atomic movie? There is Boltzmann's answer involving entropy and statistics and the anthropic principle. There is a second answer that appeals to order in the past and ultimately to the initial conditions of the universe; things just started out so as to make it that way. The Swiss physicist Walther Ritz and, more recently, the English physicist Roger Penrose, offer a third answer: 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 time's arrow. However, the more commonly accepted theory of temporal asymmetry today is that the asymmetry arises from asymmetric boundary conditions on mostly symmetric laws rather than from asymmetric laws.

Let's consider how the various arrows of time relate to each other. The direction of increasing entropy is the thermodynamic arrow. Additional arrows exist in the following processes:

a. It is easier to know the past than the future.

b. Waves spread out from, and never converge into, a point.

c. Quantum mechanical measurement collapses the wave function.

d. Kaon decay is different in a time reversed world.

e. We see black holes but never white holes.

f. Conscious actions affect the future but not the past.

g. Explanation uses the past information, not the future.

h. Causes precede their effects.

i. Higgs boson decay is different in a time reversed world.

For a process to be classified as an arrow of time, it must work differently or not at all if time were reversed. Many physicists suspect all these arrows are linked and that they must somehow involve conditions very early during the big bang.

Many physicists believe that someday the growth of physics will show that arrow i in our list is the most fundamental. The temporal asymmetry of the Higgs boson particle is already known to be the key reason why the universe contains what little matter it now does after all the primordial antimatter collided with primordial matter.

If the arrows of time are not all linked, then some may reverse while others do not. The question of whether the arrows are or are not linked is one to be settled by the physicists, not the philosophers.

There has been some controversy among physicists regarding whether the universe's expansion is an arrow of time. What is now clear is that if the universe's expansion does stop and the universe begins to collapse back upon itself, then the contraction will take place forward in time and the earlier expansion events (such as last century's World War I) won't occur in reverse order.

Duns Scotus and A. N. Prior argue that only the present is real. This presentist viewpoint maintains that the past and the future are not real. There are two camps opposed to presentism, the camp that says the past and present are real, and the camp that says the past, present, and future are real. Aristotle and C. D. Broad believe the past and present are real. Reality 'grows' with the coming into being of determinate reality from an indeterminate potential reality. Radically opposed to either of the previous two treatments of the future, Hermann Weyl, J.J.C. Smart, and others argue that the objective world simply is. There is no objective ontological difference, they say, between the past, the present, and the future just as there is no ontological difference between here and there. This position is called the "block universe" position 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.

A presentist would complain that this block universe position misses the ontologically significant point that the present is so much more 'vivid' than any other time-slice of spacetime. The advocates of the block universe counter that only the block universe can make sense of relativity's implication that an event in person A's present can be in person B's future or C's past, provided the persons are in the proper relative motion. Presentism and the growing-past theories must suppose that this event is both real and unreal because it's real for A but not real for B.

This philosophical battle between the camps has taken a linguistic turn in the 20th century by focussing upon the question, "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" and their opponents will answer "No." 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 now says, "Tomorrow the admiral will start a sea battle." 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 sentence was true all along. Truth is eternal or fixed, they say, and 'is true' is a tenseless predicate. 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't be any value in between such as 'undecided until tomorrow'. Many others, following a suggestion from Aristotle, argue that the sentence is not true until it's known to be true, namely at the time at which the sea battle occurs. The sentence wasn't true before the battle occurred. In other words, predictions have no truth values at the time they are uttered. Predictions fall into the "truth value gap." This position that contingent sentences have no truth values is called the Aristotelian position because many researchers throughout history have taken Aristotle to be holding the position--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, but it faces a series of challenges. 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.

A second 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 third challenge, from Quine and others, claims the Aristotelian position wreaks havoc with the logical system we use to reason and argue with such 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 standard of deductive validity because this standard is about the relationships among truth values of the component statements. Unfortunately, the Aristotelian position says that some of these components are neither true nor false.

In light of these various challenges to the Aristotelian position, some philosophers conclude that Aristotle should retract his claim that predictions fail to be true or false at the time they are uttered and conclude that the block universe viewpoint is correct. However, philosophers are still very divided on the issue.

What is the significance of saying that an event occured in the past, the present, or the future? There are two major answers. One answer is that these distinctions represent objective features of reality that aren't captured by the popular 'block universe' approach. This answer takes tenses very seriously and is called the tensed theory of time. A second answer is that these distinctions are subjective features of the perspective from which we view the universe. On the latter view, called the tenseless theory of time, whether the assassination of President Kennedy occurred here depends on the speaker's perspective; similarly, whether the assassination occured now is equally subjective. The proponent of the tenseless view will say that talk about the past is really talk about our own relation to events. For example, on the tenseless theory, if it's now Jan. 1, 2008 for us, then to say now that some event is past is to say that it happens [tenselessly] before all the events of Jan. 1, 2008. The goal of the tenseless theory is to provide an adequate analysis of talk about the past, the present, and the future using only talk about happens before, happens after, and happens at the same time as.

This controversy is often presented as a dispute about whether tensed facts exist, with advocates of the tenseless theory objecting to tensed facts. The primary function of tensed facts is to make tensed sentences true. For the purposes of making the point, let's uncritically accept the Correspondence Thory of Truth  , and apply it to the past tense sentence:

Custer died in Montana.

If we apply the Correspondence Theory directly to this, we would say that

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. It should be applied only to the result of analyzing tensed statements into equivalent statements that don't involve tenses, as follows:

There is a time t such that Custer dies in Montana at time t, and time t is before the time of the utterance of the sentence "Custer died in Montana."

In this analysis, the verb dies is tenseless in the same way that the verb "is" is tenseless in "7 + 5 is 12". The sentence isn't used to say "7 + 5 is presently 12." Ditto for the verb is in the above phrase "time t is before...." Applying the Correspondence Theory to this new sentence will produce:

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 of "Custer died in Montana."

Advocates of the subjective theory of tenses, D. H. Mellor, for example, argue that the truth conditions of any tensed sentence can be explained without tensed facts even if some tensed sentences can't be translated into tenseless ones. And 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. 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 tensed talk; but the analysis shows that ordinary tenseless facts are adequate.

This analysis of tenses is challenged. It can work only for utterances, but a sentence can be true even if never uttered by anyone. Even if that problem could be repaired, there are other challenges, especially involving demonstratives and indexicals. For example, Roderick Chisholm and A. N. Prior claim that the 'is' in the sentence "It's 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 n such that n = midnight" is to miss the essential reference to the present in the original sentence. The latter sentence is always true, but the original is not. There is no escape by adding "and n is now" because this last indexical still needs analysis, and we've gone in a circle.

Chisholm and Prior say that true sentences using the temporal indexical terms 'now,' 'before now,' and 'happened yesterday' are part of the facts of the world that science should account for, but science fails to do this because it doesn't recognize them as being real facts. Science so far restricts itself to eternal facts, such as in the Minkowski-like spacetime representation of events. These events are sets of spacetime points. For such events, the reference to time and place is explicit. A Minkowski spacetime diagram displays only what happens before what, but not which time is present time, or past, or future. What is missing from the diagram, say Chisholm and Prior, is some moving point on the time axis representing the observer's 'now' as time flows up the diagram.

In the same spirit, Michael Dummett argues that you can have a complete description of a set of objects in space even if you haven't said which objects are near and which are far, but you cannot have a complete description of those objects without specifying which events are present and which are not.

Russell, Quine, Grunbaum, and Horwich object to assigning special ontological status to the present. According to Quine, the analysts 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 aren't 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.

In the 1950s, A. N. Prior created a new symbolic logic to describe our use of time words such as 'now', 'happens before', 'afterwards', 'next', 'always', and 'sometimes'. He was the first to appreciate the similarity in structure between time concepts and modal concepts such as 'it is possible that' and 'it is necessary that.' He applied a logic having infinitely many truth-values to create a 'tense logic' in which the relationships that propositions have to the past, present, and future help to determine their truth-value. In classical logic, there are only two truth-values, namely true and false. Dummett and Lemmon also made major, early contributions to tense logic. In one standard system of the logic of past time, the S4.3 system, 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 'M' represent this operator, and add to the axioms of classical propositional logic the modal axiom M(p v q) iff Mp v Mq. The axiom says that for any two 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. S4.3's key axiom is the equivalence

Mp & Mq iff M(p & q) v M(p & Mq) v M(q & Mp).

This axiom captures our ordinary conception of time as a linear succession of states of the world. Logicians disagree about what additional axioms and revisions are needed to make more of our beliefs about time be theorems of a symbolic logic of time.

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 suggestions that future contingent sentences don't 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 predictions, 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 true and falsehood.

References and Further Reading:

Bondi, Hermann. “The Space Traveler’s Youth,” Discovery, Dec. 1957, pp. 505-510.

This popular article includes a description of the Halsbury version of the twins paradox with all clocks in inertial frames.

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.

Gell-Mann, Murray. The Quark and the Jaguar, W. H. Freeman and Co., 1994.

A Nobel Prize winning physicist discusses time's arrow in chapter 15.

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.

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.

Price, Huw.Time's Arrow and Archimedes' Point, Oxford University Press, 1996.

This technical monograph adopts the block universe view and argues that physicists have failed to achieve the Archimedean standpoint that is required for a proper understanding of time's asymmetry.

Prior, A. N. Past, Present and Future, Oxford University Press, 1967.

A pioneering work in temporal logic, the symbolic logic of time.

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 aren't real.

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 twins paradox or clock paradox.

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.

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 book.

Bradley Dowden
Philosophy Department

California State University - Sacramento