Physics' Big Puzzle Has Big Question: What Is Time? By JAMES GLANZ

STILLWATER, MN Jun 19 01  When philosophers debate the nature of time and space, a listener is liable to walk away muttering something like "Whoa..." On the same question, a technical exchange among scientists is more likely to elicit a "Huh?" A conference here this month brought together both camps to explore that question  which happens to lie at the heart of the most important unsolved problem in physics  in the hope of bringing forth a satisfying "Aha!" of discovery.

That problem is the search for a theory that encompasses both the effects of gravity, described by Einstein's theory of general relativity, and the fuzziness that occurs in the realm of tiny particles according to quantum mechanics. For a century, technical difficulties have frustrated all attempts to develop a theory that holds where both gravity and quantum effects are crucial, like at the centers of black holes or during the first moments of the Big Bang explosion in which the universe is thought to have originated.

The conference, called the Seven Pines Symposium, drew together some two dozen physicists, historians and philosophers. It was in part an effort to step back from the technical morass and identify the roots of the problem. As the four-day meeting developed, it became clear that those roots run so deep that time  and to a lesser extent, space  may not even be the same actors in unified theories based primarily on relativity as in those based on quantum mechanics. In short: "Arrrgh."

"Many approaches have run into major stumbling blocks that seem to require some new understanding of space and time," said Prof. Robert Wald, a physicist at the Univ of CHI. Calling on the image of blind men feeling their way around an object, Prof Wald said, "I don't see any evidence that they're talking about different parts of the same elephant."

Professor Wald was quick to add that the conference should not be seen as a desperate move by scientists to seek philosophical enlightenment on questions that have stymied the physicists. But another physicist, Prof. Abhay Ashtekar of Penn State, where he is director of the Center for Gravitational Physics and Geometry, conceded that "there is a little bit of shaking of confidence" among scientists thirsty for a breakthrough.

"That's the whole point in stepping back," Professor Ashtekar said. "I think somehow the mind is becoming a little more open to ideas coming from everywhere else."

The historians and philosophers occasionally led the scientists on a merry chase through foreign terrain. Prof. John Earman, who is in the hist and philosophy of science dept at the Univ of Pitt, said the structure of relativity theory suggested that time could merely be a "psychological illusion" that was important to humans but not a fundamental element of any unified theory.

At this, Prof. Serge Rudaz, a physicist at the Univ of Minn, started looking around the room in surprise. "That sounds pretty radical to me," he said. "Am I the only one?" He was not. But another philosopher, Prof. Nick Huggett of the Univ of IL at CHI, suggested that success could be near. It was precisely by struggling, and occasionally blundering, with basic definitions of space and time that great scientists like Newton and Descartes made crucial progress in framing less ambitious theories, he said.

"These thinkers faced similar problems to those encountered today in the development of quantum theories of gravity," Prof Huggett wrote in an introduction to his talk. Although no immediate resolution appeared, the symposium did call into sharp relief the problem of exactly what time is, a question whose solution, said Prof. Karel Kuchar, a physicist at the Univ of Utah, "is simply the wind that precedes the storm of any future theory."

The crux of their problem is that time itself looks very different depending on whether scientists try to construct a final theory by starting with quantum mechanics and adding gravity, or vice versa.

For all their strangeness and sophistication, including predictions that a particle can be in many places at once or have irreducibly uncertain speeds and positions, theories based on quantum mechanics and particle physics assume that somewhere, the regular tick-tock of ordinary time is being measured by something like a Swiss watch or a planet whirling around a star.

That crutch is a legacy of the classic formulation of quantum mechanics, which divides the universe into "observers" who make measurements and particles that are measured. Relativity theory could not be more different, focusing on how the gravity of massive bodies bends the structure of time and space. Like marbles rolling on a warped rubber surface, the bodies then move about in ways determined by the bending of space-time, and so on: everything is dealt with together, including any observers.

That is why if scientists go in the other direction and "quantize" relativity theory, they end up with a theoretical universe in which not only particles, but also time and space themselves are shifting and indeterminate, as elusive as the ripples on the bottom of a pool.

Although many physicists expect that the universe really does shift and shimmer on tiny scales, where quantum effects should bend space- time just as gravity does on large scales, the absence of a reliable "background" means that there is no Swiss watch, even in theory, for the particle physicists.

Nevertheless, Prof. Jeffrey Harvey of the Univ of CHI said he believed that string theory  a particle theory whose ambitious goal is to explain all the known forces in nature as different facets of the same diamond, so to speak  is by far the best bet for unifying physics. 

Roughly speaking, the theory assumes that the vibrations of unimaginably tiny objects called strings and branes correspond to all particles that have so far been discovered, along with a slew of others that have not. The vibrating thingies supposedly exist in many more dimensions than the four that humans are familiar with, but the extra ones are considered to be somehow curled up like arthritic fingers and so small that they are not apparent.

Because all force-carrying particles are included, including gravitons, which theoretically transmit gravity, string theory has the potential to unify all of physics. But because it exists so far only in fragmentary form, Professor Harvey said, string theory must assume that a particular space-time background exists, rather than letting one emerge naturally from the interactions of the particles.

"If you ask a string theorist, `Tell me how to formulate your theory in a way that doesn't involve any choice at all of a background space-time,' they throw up their hands and say, `We don't know how to do that,' " Professor Harvey said.

But the relativity theorists don't have it any better. For them, time and space begin to mix together in incomprehensible ways when quantum effects are added to Einstein's equations. In essence, they often cannot even find time as an entity distinguishable from space in the mathematical mishmash that results. "Relativity glued almost everything to everything else," said Prof Kuchar, of the Univ of Utah, and the consequence is head- spinning confusion when quantum mechanics is added to the theory.

The problem could mean that quantum relativity is simply wrong, that time is not so important after all or that a new definition of time in the quantum realm must emerge. It could be, in Professor Earman's somewhat chilling conjecture, that time is an illusion important only to humans, not to physics.

One possibility, said Professor Wald, of the Univ of CHI, is that time will ultimately have meaning only as correlations between events. For example, cosmic events like a stellar explosion could be referred to the size of the ever-expanding universe at the moment they happened, rather than to some abstract notion of pure time. But even then, "one runs into all sorts of obstacles," Professor Wald said.

In a sense entirely appropriate to a philosophical gathering, the participants seemed to agree only on what time could not be. But the symposium had a surprising ending when Prof Ashtekar, rather than one of the philosophers, turned to poetry for a note of hope. The Chinese sage Lao Tsu, he said, looked at time and space in a way that might apply to string theory and relativity:

These two spring from the same source but differ in name; this appears as darkness. Darkness within darkness. The gate to all mystery.

Time has been studied by philosophers and scientists for 2,500 years, and although time is much better understood today than long ago, many mysteries remain. This article explores both what is known about time and what is controversial and unresolved. The focus is on physical time, the time that clocks measure, rather than on psychological time, a human being's perception of physical time. The article is structured so that it provides answers to the following questions about physical time: What should a philosophical theory of time do? What is time? What does science require of time? What sort of time travel is possible? What is the relational theory of time? Does time flow? Why does time have an arrow? Are there essentially tensed facts? Is the future real? What is the symbolic logic of time? What is a reference frame? What is spacetime? What is an event? Does the theory of relativity imply time is partly space? Is time the fourth dimension? Is time infinite? Is there more than one kind of physical time? How is time relative to the observer? What are the relativity and conventionality of simultaneity? What is the difference between the past and the absolute past? What is time dilation? How does gravity affect time? What happens to time near a black hole? What is the solution to the twins paradox? What is the solution to Zeno's paradoxes? How do time coordinates get assigned to points of spacetime? How do dates get assigned to actual events? What is essential to being a clock? What is our standard clock? Why are some standard clocks better than others?

What should a philosophical theory of time do? Can we begin with a definition of time? Succinct definitions of time are rarely helpful unless they are backed up with a more systematic treatment of time. The definitions are either too trivial (Time is what keeps everything from happening all at once) or too vague (Time is the dimension of causality) or too circular (Time is what happens when things change over time) or simply cryptic (Time is the flow of events past the stationary I). When philosophers ask, " What is time?", they normally are also asking for a 'definition' that provides something more elaborate, for a philosophical theory designed to answer many of the philosophical questions about time. Consider what a more systematic theory of time should do. It should reveal, among other things, whether time exists objectively, or is instead a construct of our imagination. 

A theory of time should be able to say what physical science presupposes and implies about time. Does it imply the possibility of time travel, for instance? What does it imply about the relationship between time and spacetime? What is the largescale and the smallscale structure of time? In the smallscale, what is time made of? Physicists say that, locally, time is made of a linear continuum of instants, with each instant lasting for zero seconds. A philosophical theory will say whether the physicists are merely inventing this notion of time because it is useful or, instead, are discovering what time is. Being a continuum implies that between any two instants, there is another instant. No scientific experiment 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. relational theories of time. 

A theory of time should address the question of time's apparent direction. If the projectionist in the movie theater showsa film of milk 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: brown coffee never unmixes into black coffee and milk. 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 there are hardly any arrows (asymmetries in time) in the most basic laws of physics that arre supposed to accurately describe the one-directional processes of nature. 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 now is real, then why isn't there a term for it in the laws of science? On the other hand, some argue that the lack of this term reveals a limitation on what science can tell us about reality. 

For a last example of a philosophical problem regarding time, some philosophers argue that the future is not real. 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 not only this issue but also the previously mentioned constellation of philosophical issues about time. Definitions of time

There are a wide variety of short answers to the question "What is time?" Plato said time is the circular motion of the heavens. Aristotle said it's not motion but the measure of motion. 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. Kant said time is a form that the mind projects upon the external things-in-themselves. A modern definition says time is the dimension of causality. Let's explore some of these answers.

Aristotle provided an early, careful answer to the question "What is time?" when he said 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] In these passages, Aristotle argues that time 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. Time is like a line, he says; and it is continuous rather than discrete. The line he had in mind was a circle [223b], a structure that has no beginning or end point and so is endless in both directions.

 Saint Augustine 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. Thomas Aquinas agreed. In 1687, Newton captured some of this viewpoint when he represented time by using a line rather than a circle. Aristotle argued that we cannot conceive of a first time because for any such time we could conceive of a time before that. Thomas Aquinas criticized the assumption that something doesn't exist if humans can't conceive it. 

Aristotle raised the issue of whether time exists without consciousness: "Whether, if soul 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, 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 while we are waiting for the water to boil on the stove. We are referring to physical time when we speak of the time that a clock measures, or when we define speed to be the rate of change of position with respect to 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. 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, but Duns Scotus in the 13th century recognized both physical and psychological time.

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 added that motion (your speed, for example) is relative to the reference frame you are analyzing it from, but that there is a special reference frame in which real time (absolute time) is the measured time. Newton also argued very specifically that time and space are substances that provide an infinitely large container for all events; this container is the absolute reference frame. Gottfried Leibniz objected. 

He argued that time is not a substantial entity existing independently of those events. Leibniz insisted that Aristotle and Newton had overemphasized the relationship between time and duration, and underemphasized the fact that time ultimately involves order as well. Time is an ordering of changes, the overall ordering of all non-simultaneous events. Leibniz added that this order is also a "something" as Newton had been insisting, but it is an ideal entity, not a concrete one as Newton was mistakenly supposing it to be. Trees and stars are concrete entities. Triangles, numbers, and relations are 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. One proper, but indirect, 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 physics. Many philosophers complain that this answer is incomplete because, although philosophical theories of time should be informed by what science requires of time, they should progress beyond.

What science requires of time Quantum field theory and Einstein's general theory of relativity are the most fundamental theories of physics. According to 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 Minkowski 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.

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.

For example, suppose a bolt of lightning strikes the front of a speeding train and another strikes the back of the train. The train conductor, who is sitting in the middle of the train, tries to determine whether the two lightning bolts struck simultaneously. If the two flashes from front and back reach the conductor at the same instant, they did. According to Einstein's definition of simultaneity for two events occuring at different places, light rays coming from those two events will reach the midpoint between them at the same time. The train conductor is at the midpoint of the train. You, however, are at rest on the platform beside the train track just as the two flashes reach the conductor. They reach you at the same instant as well, but you will judge that neither you nor the conductor are at the midpoint between the two events; you are merely at the midpoint of the train. 

From your perspective (reference frame), you will point out that the conductor is speeding toward the place where the front lightning bolt struck. By the time the light reaches him (and you), he is closer to the front strike, so the lightning must have struck the back of the train before it struck the front. You will judge that the two events were not simultaneous. Einstein says both of you are correct in your apparently contradictory judgments about simultaneity. This feature of our universe is what Einstein calls the "relativity of simultaneity." The events really are simultaneous in the reference frame fixed to the train, and the events really are not simultaneous in the reference frame fixed to the track. This relativity is a relativity for distant events, 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, the values of the time variable t are real numbers, with each number designating an instant of time. Time is a linear continuum of instants, similar to the mathematician's line segment. Therefore, 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 it 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.

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 support for the claim that between any two events there is a third. 

The support comes from the fact that the assumption of continuity in the general theory of relativity and in quantum theory is convenient and useful, and it rests on the fact 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. That is, 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.

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 actually 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 here, the astronomers now conclude that about twelve to fifteen billion years ago the universe was in a state of infinite density and zero size. Because all substances cool when they expand, physicists believe the universe itself must have been cooling down over the last twelve to fifteen billion years. Therefore, the universe started out very hot and very small. 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 come 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 past, and the term "the big bang" refers to the very early events, not to a single event. The remainder of this article we will speak casually of 'the' big bang event in order to simplify the discussion.

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 demand for a scientific justification or in 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, 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.

Relativity theory implies there is time 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. These relationships call for treating the twins paradox with general relativity, not with special relativity.

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 in the direction of a black hole, time slows on approach to the event horizon, and it completely stops at the center of the hole--relative to time on a clock that remains safely back on Earth. As an astronaut swiftly falls into the hole, the proper time, the time measured on the astronaut's clock, passes beyond the end of our civilization's time. 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.

The determinate reality of the future Are predictions true or false when uttered? Suppose someone yesterday said, "Tomorrow there will be a sea battle." If you, the admiral, choose to start a sea battle today, you will make the sentence be true. Many philosophers argue that in this case the sentence was true all along. 

Truth is eternal or fixed, they say, and "is true" is a tenseless predicate. The ancient Greek philosopher Chrysippus was convinced that a contingent sentence about the future is either true or it is false and not any value in between. Many others, following Aristotle's lead, argue that the sentence (that is, the proposition or statement made using the sentence) isn't true until the time at which the sea battle occurs. The sentence wasn't true yesterday. In other words, predictions have no truth values at the time they are uttered. A principal motivation for adopting the Aristotelian position is the belief that if future statements involving 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 first person to give a clear presentation of the implications of treating predictions as being neither true nor false was the Polish logician Jan Lukasiewicz in 1920. To carry out Aristotle's suggestions, he developed a three-valued symbolic logic, with all grammatical sentences having the truth-values of true, false, or else indeterminate. Contingent sentences about the future, such as predictions, are assigned the indeterminate truth-value.

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 complains that the Aristotelian position makes the future be presently unreal. There is no determinate reality to the future if statements about the future have no truth values. 

This lack of determinate reality is unacceptable because special relativity implies that some events in one person's present can be in another person's future, if the two persons are in relative motion. Surely Aristotelians are mistaken if they suppose some persons' presents are real and other persons' presents are not, argued Hilary Putnam. Putnam believes future things are real, even if they do not exist yet; and the real things are all those that will exist, do exist, or have existed. Putnam disagrees with Duns Scotus who argued that only the present is real and with Aristotle who argued that only the present and past are real. Agreeing with Putnam, Quine adds a moral argument. 

The determinate reality of the future is assumed in moral discussions about the interests of people who are as yet unborn. 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. 

Yet another challenge to the Aristotelian position comes from Quine and others who claim that it wreaks havoc with the logical system we use to reason and argue with such predictions. For example, here is a deductively valid argument: We've learned there will be a sea battle tomorrow. If there will be a sea battle tomorrow, then the admiral should be awakened. So, the admiral should be awakened.

Without the sentences in this argument being true or false we cannot properly assess the argument using the standards of deductive validity and invalidity, despite the work by Lukasiewicz. Yet the Aristotelian position says these sentences aren't true or false. In light of these various challenges to the Aristotelian position, many philosophers conclude that Aristotle should revise his belief that predictions fail to be true or false at the time they are uttered. The symbolic logic of time 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", "sometimes", and so forth. He was the first to appreciate the similarity in structure between time concepts and modal concepts such as "it is possible." 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.

SUPPLEMENT This supplement answers a series of questions designed to reveal more about what science requires of physical time, and to provide background information about other topics discussed in this article.

What is a reference frame? A reference frame is a point of view, a perspective for making observations and judgments. Special relativity is intended to apply only to inertial reference frames. Inertial frames are reference frames in which Newton's first law of inertia holds: any object's acceleration is zero if no net force acts on the object. In other words, if no unbalanced external forces are acting on a moving object, then the object moves in a straight line. It doesn't curve or go into orbit. And it travels equal distances in equal amounts of time. Any frame of reference moving at constant velocity relative to an inertial frame is also an inertial frame. A reference frame spinning relative to an inertial frame isn't an inertial frame. 

The presence of gravitation normally destroys any possibility of finding a frame that is a perfect inertial frame, but a reference frame in which the 'fixed' stars are at rest is approximately an inertial reference frame, as is any reference frame moving at constant velocity with respect to the 'fixed' stars. Is a reference frame attached to Earth an equally good approximation to an inertial reference frame? Not quite. The frame is spinning relative to the heavenly bodies; and the gravitational forces due to the Moon, Sun and planets will make Newton's law fail; but for many situations these influences are negligible, and computations using special relativity or even Newton's mechanics give fine results.

What is spacetime? Spacetime is a certain 4-d space (or 4-d manifold, to use Riemann's term for space). It's the 4-d continuum we live in. Spacetime is the intended model of the general theory of relativity. This requires it to be a differentiable space in which certain geometrical objects obey the covariant field equations of general relativity, and in which physical objects obey the equations of motion of the theory. The metaphysical question of whether spacetime is a substantial object or a relationship among events, or neither, is taken up in the discussion of the relational theory of time. Regardless of how that question is answered, spacetime is more fundamental in science than either space or time alone. Einstein's general theory of relativity (1915) assumes that spacetime is fundamental, with space and time being two distinct sub-spaces of it. 

Spacetime is a continuum in which we can define points and straight lines. However, these points and lines do not satisfy the principles of Euclidean geometry. Einstein's principal equation in his general theory of relativity implies that the curvature of the geometry of spacetime is directly proportional to the density of mass in the spacetime. The equation can be interpreted as implying that matter causes curvature in the spacetime geometry, or vice versa. The region of spacetime at the center of a black hole develops infinitely large curvature. Curvature of spacetime is a curvature of its space part, not its time part. Mass doesn't cause time to curve.

Regions of spacetime are frequently pictured with a Minkowski diagram using a rectangular coordinate system. The vertical 'time' axis is the product of time and the speed of light so that world lines of light rays leaving the origin make a forty-five degree angle with any space axis. The Minkowski diagram applies to a particular observer who experiences the event that occurs at the point indicated by the diagram's origin. In a Minkowski diagram, an ideally small physical particle is not represented as occupying a point of spacetime but as occupying a line containing all the spacetime points at which it exists. The line is called the "world line" of the particle. If two world lines intersect, then the two particles have collided. A person's world line is composed of the world lines of the person's component particles. Inertial motion corresponds to straight world lines, and accelerated motion corresponds to curved world lines.

Although relativity theory assumes that spacetime is fundamental, there have been serious attempts over the last few decades to construct theories of physics in which spacetime is not fundamental but is a product of more basic entities such as superstrings. The primary aim of these new theories is to unify relativity with quantum theory, but so far these theories have not stood up to any empirical observations or experiments that could show them to be superior to the presently accepted theories. So, spacetime remains fundamental.

What is an event? An event might be defined simply as whatever is temporally before or after anything else. In ordinary discourse, an event is a happening during which some object changes its properties. The event of the buttering of the toast involves the toast's changing from having the property of being unbuttered to having the property of being buttered. In ordinary discourse, an event has more than an infinitesimal duration, but in the technical discourse of physics, all events are composed of point events. A point event is a spacetime point's having some property other than those it has just by being a location in spacetime. The point event is the having of some property at some point in space for an instant, with no change required. For example, there is the event of a certain point in spacetime having butter. The macroscopic event of a buttering of toast is composed of an infinite number of point events involving the butter and toast. 

Although point events can be defined in terms of objects and properties and times in this way, point events and spacetime points actually are more basic in physics than are objects and properties. Point events are what all objects and events are made of, and spacetime points are what have the properties. The later Einstein moved away from the relational theory of time to the position that material objects are 'funny' places in the field, with the field itself being spacetime as characterized by the metric and stress-energy tensors. 

These metaphysical assumptions of modern science are not part of common sense, the shared background beliefs of most people. They also are not acceptable metaphysical assumptions for many philosophers. In 1936, Bertrand Russell and A. N. Whitehead developed a theory of time based on the assumption that all events in spacetime have a finite duration. However, they had to assume that any finite part of an event is an event, and this assumption is no closer to common sense than the physicist's assumption that all events are composed of point events.

Does the theory of relativity imply time is partly space? In 1908, when Minkowski remarked that "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," many people took this to mean that time is partly space, and vice versa. C. D. Broad countered that the discovery of spacetime did not break down the distinction between time and space but only their independence or isolation. He argued that their lack of independence does not imply a lack of reality. 

The Broad-Minkowski disagreement is still an issue in philosophy, but if Broad is correct, then time is time; it's not space at all. Nevertheless, there is a deep sense in which time and space are 'mixed up' or linked. This is evident from the Lorentz transformations of special relativity that connect the time t in one inertial frame with the time t' in another frame that is moving in the x direction at a constant speed v. The relationship is t' = [t - vx/c]/[square root(1- v/c)]

In this equation, t' is dependent upon the space coordinate x and the speed. In this way, time is not independent of either space or speed. It follows that the time between two events could be zero in one frame but not zero in another. Each frame has its own way of splitting up spacetime into its space part and its time part. The reason time is not partly space is that time is not simply an arbitrary one-dimensional sub-space of spacetime; it is a distinguished sub-space. That is, time is a distinguished dimension of spacetime, not an arbitrary dimension. What being distinguished amounts to is that when you set up a rectangular coordinate system on spacetime with an origin at the signing of the Declaration of Independence in Philadelphia, you can point the x-axis east or north or up or anywhere in between, but you are not allowed to point it forward in time--you can do that only with the t-axis, the time axis.

Is time the fourth dimension? Yes and no; it depends on what you are talking about. Time is the fourth dimension of spacetime, but time is not the fourth dimension of the space of places. Mathematicians have a broader notion of the term "space" than the average person; and in their sense a space need not consist of places, that is, geographical locations. Not paying attention to the two meanings of the term "space" is the source of all the confusion about whether time is the fourth dimension. The 'space' of spacetime is four dimensional and in that space, the space of places is a 3-d sub-space. But spacetime is a space of events, not a space of places. 

In any coordinate system on spacetime, it takes at least four independent numbers to determine a spacetime location. In any coordinate system on the space of places, it takes at least three. That's why spacetime is four dimensional but the space of places is three dimensional. Actually this 19th century definition of dimensionality, which is due to Bernhard Riemann, is not quite adequate because mathematicians have subsequently discovered how to assign each point on the plane to a point on the line without any two points on the plane being assigned to one point on the line. Consequently, the line and the plane have the same number of points, and the line and plane must have the same dimensions according to the definition. To avoid this problem, the dimensionality of a space has been given a rather complex new definition. Is time infinite?

There are three ways to interpret this question: (a) Was there an infinite amount of time in the past? No, not if time began with the big bang. (b) Is time infinitely divisible? Yes, because general relativity and quantum mechanics require time to be a continuum. (c) Will there be an infinite amount of time in the future? This is difficult to judge. First, can time exist without events? If so, the future is infinite. If not, then we need to know whether events will keep occurring. The best estimate from the cosmologists these days is that the expansion of the universe will continue forever. There always will be the events of particles getting farther apart, and so future time will be infinite.

Is there more than one kind of physical time? Every reference frame has its own physical time, but the question is intended in another sense. At present, physicists measure time electromagnetically. They define a standard atomic clock using periodic electromagnetic processes in atoms, then use electromagnetic signals (light) to synchronize clocks that are far from the standard clock. In doing this, are physicists measuring 'electromagnetic time' but not other kinds of physical time? In the 1930s, the physicists Arthur Milne and Paul Dirac worried about this question. Independently, they suggested there may be very many time scales.

 For example, there could be the time of atomic processes and light, which is measured best by atomic clocks. There also could be the time of gravitation and large-scale physical processes, which is measured best by the rotation of a pulsar (pulsating star). The two physicists worried that the atomic clock and the astronomical clock might drift out of synchrony after being initially synchronized, yet there would be no reasonable explanation for why they don't stay in synchrony. Ditto for clocks based on the pendulum, on superconducting resonators, on the spread of electromagnetic radiation through space, and on other physical principles. Just imagine the difficulty for physicists if they had to work with electromagnetic time, gravitational time, nuclear time, neutrino time, and so forth. Current physics, however, has found no reason to assume there is more than one kind of time for physical processes. 

In 1967, physicists did reject the astronomical standard for the atomic standard because the deviation between known atomic and gravitation periodic processes could be explained better assuming that the atomic processes were the more regular of the two. Physicists had no reason to believe that a gravitational periodic process, that is just as regular initially as the atomic process and that is not affected by friction or impacts or other forces, would ever drift out of synchrony with the atomic process, yet this is the possibility that worried Milne and Dirac.

How is time relative to the observer? Physical time is not relative to any observer's state of mind. Wishing time will pass does not affect the rate at which the observed clock ticks. On the other hand, physical time is relative to the observer's reference system--in a trivial way and in a deep way. 

In a trivial way, time is relative to the chosen coordinate system on the reference frame, though not to the reference frame itself. For example, it depends on the units chosen as when the duration of some event is 34 seconds if seconds are defined to be this long, but not if they are defined to be that long. Similarly, the difference between the Christian calendar and the Jewish calendar for the date of some event is due to a different unit and origin. Also trivially, time depends on the coordinate system when a change is made from the Eastern Standard Time to Pacific Standard Time. 

These dependencies are ignored when scientists measure the duration of a process that would be affected by them. For example, if a pendulum's approximately one-second swing is measured in a physics laboratory during the autumn night when the society changes from Daylight Savings Time back to Standard Time, the scientists do not note that one unusual swing of the pendulum took a negative one hour instead of the usual one second.

In a deeper sense there is relativity to the reference frame and not just to the coordinate system on that frame. That is Einstein's principal original idea about time. To illustrate for special relativity, let's assume that a number of observers are at rest in their inertial frames of reference. Which of these observers will agree on their time measurements? Observers with zero relative velocity will agree. Observers with different relative velocities will not, even if they agree on how to define the second and agree on some event occuring at time zero (the origin of the time axis). All observers will be observing the same objective reality, the same spacetime, but their different frames of reference will require disagreement about how spacetime divides up into its space part and its time part.

Relative to any observer, was Adolf Hitler born before George Washington? No, because the two events are causally connectible. That is, one event could in principle have affected the other since light would have had time to travel from one to the other. We can select a reference frame to reverse the usual Earth-based order of two events only if they are not causally connectible. Despite the relativity of time to a reference frame, all observers should agree about what happens before what when it comes to describing causally connectible events.

What are the relativity and conventionality of simultaneity? Events that occur simultaneously with respect to one reference frame may not occur simultaneously in another reference frame that is moving with respect to the first frame. This is called the "relativity of simultaneity," but this philosophically uncontroversial feature of time is different from the philosophically controversial feature called the "conventionality of simultaneity."

Given two events that happen essentially at the same place, physicists assume they can tell by direct observation whether the events happened simultaneously by direct observation. If we don't see one of them happening first, then we say they happened simultaneously, and we assign them the same time coordinate. The determination of simultaneity is more difficult if the two happen at separate places. One proper way to measure (operationally define) simultaneity at a distance is to say that two events are simultaneous in a reference frame if unobstructed light signals from the two events would reach us simultaneously when we are midway between the two places where they occur, as judged in that frame. This is the operational definition of simultaneity used by Einstein in his theory of relativity.

The 'midway' method described above of operationally defining simultaneity in one reference frame for two distant signals causally connected to us has a significant presumption: that the light beams travel at the same speed regardless of direction. Einstein, Reichenbach and Grnbaum have called this a reasonable "convention" because any attempt to experimentally confirm it presupposes that we already know how to determine simultaneity at a distance. This is the conventionality, rather than relativity, of simultaneity.


To pursue the point, suppose the two original events are in each other's absolute elsewhere; they couldn't have affected each other. Einstein noticed that there is no physical basis for judging the simultaneity or lack of simultaneity between these two events, and for that reason said we rely on a convention when we define distant simultaneity as we do. Hillary Putnam objects to calling it a convention--on the grounds that to make any other assumption about light's speed would unnecessarily complicate our description of nature, and we often make choices about how nature is on the basis of simplification of our description. Putnam would say there is less conventionality in the choice than Einstein supposed.

The 'midway' method isn't the only way to define simultaneity. Consider a second method, the 'mirror reflection' method. Select an Earth-based frame of reference, and send a flash of light from Earth to Mars where it hits a mirror and is reflected back to its source. The flash occurred at 12:00, let's say, and its reflection arrived back on Earth 20 minutes later. The light traveled the same empty, undisturbed path coming and going. At what time did the light flash hit the mirror? The answer involves the so-called conventionality of simultaneity. All physicists agree one should say the reflection event occurred at 12:10. The controversial philosophical question is whether this is really a convention. 

Einstein pointed out that there would be no inconsistency in our saying that it hit the mirror at 12:17, provided we live with the awkward consequence that light was relatively slow getting to the mirror, but then traveled back to Earth at a faster speed. If we picked the impact time to be 12:05, we'd have to live with the fact that light traveled slower coming back. There is a physical basis for not picking the impact time to be less than noon nor later than 12:20, because doing so would violate the physical principle that causes precede their effects. One requirement we place on the concept of simultaneity is that distant events which are simultaneous could not be in causal contact with each other. We can satisfy that requirement for any choice of impact time from 12:00 to 12:20.

What is the difference between the past and the absolute past? The events in your absolute past are those that could have directly or indirectly affected you, the observer, now. These are the events in or on the backward light cone of your present event, your here-and-now. The backward light cone of event E is the imaginary cone-shaped surface of spacetime points formed by the paths of all light rays reaching E from the past. An event's being in a point's absolute past is a feature of spacetime itself because the event is in the point's past in all possible reference frames. The feature is frame-independent. For any event in your absolute past, every observer in the universe (who isn't making an error) will agree the event happened in your past. Not so for events that are in your past but not in your absolute past. Past events not in your absolute past will be in what Eddington called your "absolute elsewhere." This is the region of spacetime containing events that are not causally connectible to your here-and-now. For example, the

 A Minkowski spacetime diagram displays what happens before what, but not which time is present time. What is missing from the diagram is some moving point on the time axis representing the observer's "now." 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, Grnbaum, and Horwich object to assigning special ontological status to the present. According to Quine, logicians dealing with time and philosophical analysts of language dealing with talk involving tense should in principle be able to eliminate the temporal indexical words because their removal is needed for fixed truth and falsity of our sentences, 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. If attention is paid to how we normally use the term "fact," then the sentence "Event E is happening now (in reference frame R)" doesn't really express a fact. According to those who oppose assigning special ontological status to the present, facts must hold simpliciter, not relative to an observer's experience. Sentences expressing facts must have a fixed truth. 

The sentence "Custer's death in Montana happened a long time ago" isn't a fact because it's true for us but not for Custer's contemporaries. Unless there's a good reason to change what we mean by the very word "fact," the sentences "Event F is past" and "It's now midnight" are not on the list of facts of the world. What are on the list are the sentences "Custer's death in Montana happened before Hitler's death in Berlin" and "Event E occurs before the event F in reference frame R." These sentences are fixed truths or eternal truths. Grammatically, the two verbs "happened" and "occurs" in the two sentences are past tense and present tense, respectively, but logically they occur tenselessly