1. Time vs. “Time”

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

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

  1. Defining Time Order with Causal Order

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

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

  1. Linear and Circular Time

During history, a variety of answers have been given to the question of whether time is like a line or, instead, like a circle. The concept of linear time first appeared in the writings of the Hebrews and the Zoroastrian Iranians. The Roman writer Seneca also advocated linear time. Plato and most other Greeks and Romans believed time to be motion and believed cosmic motion was cyclical, but this was not envisioned as requiring any detailed endless repetition such as the multiple rebirths of Socrates. However, the Pythagoreans and some Stoic philosophers did adopt this drastic position.

If your personal time were circular, you could be assured that after your death you would be reborn. The future becomes the past. If time is like this, then the question arises as to whether there would be an endless number of times when each state of the world reoccurred, or whether, accepting Leibniz’s Principle of the Identity of Indiscernibles, each supposedly repeating state of the world would occur just once because each state would be not be discernible from the repeated state.

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

  1. Does Time Emerge from Something More Basic?

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

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

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

  1. What Does Science Require of Time?

The three fundamental theories of physics, namely relativity, quantum mechanics and the Big Bang theory, all imply that any duration is a continuum like a segment of the real number line, so time is not atomistic or discrete. Spacetime is more fundamental than either space or time alone, although time is not space because time is a distinguished, linear subspace of four-dimensional spacetime. Unlike in Newton’s physics and the physics of special relativity, spacetime is not a passive container for events; it is dynamic in the sense that changes in matter-energy can change the curvature of spacetime itself. The duration of an event depends on the reference frame used in measuring the duration; and so does the order in which two events occur, although all observers agree on the time order of two events that could be causally related. Relative to clocks that are stationary in the reference frame, clocks in motion run slower, and so do clocks in higher gravitational fields. In general, two synchronized clocks do not stay synchronized if they move relative to each other or undergo different gravitational forces. According to the classical Big Bang theory of cosmology, the universe has a finite past, having begun 13.7 billion years ago as spacetime expanded from an infinitesimal beginning. For an expanded discussion of these compressed remarks, see What Science Requires of Time.

  1. What Kinds of Time Travel Are Possible?

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

According to relativity theory, there are two ways to travel into the future—either by moving at high speed or by taking advantage of the presence of an intense gravitational field. If you have a fast enough spaceship, you can travel to the year 2,300 C.E. on Earth (as measured by Earth-based clocks and calendars) while your own clock measures much less elapsed time. You can affect that future, not just view it. But you can not get back to the twenty-first century on Earth by reversing your velocity or reversing the gravitational field. People who live in the ground floor apartment age slower than their twin who lives in the top floor of the same building, although the time travel is more noticeable if the younger twin lives near a black hole than simply nearer the Earth. If you engage in either sort of travel to the future, you are always in your own present during the traveling; you don’t leap into your own future or anyone else’s future.

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

Although time travel to the past apparently is consistent with Einstein’s general theory of relativity, there are several well known arguments against the possibility. None are generally considered to be decisive. Here are the arguments:

  1. If you encountered someone who claimed to be a time traveler, what could you do to verify the claim? There’s nothing you could do, therefore there will never be a good reason to believe in time travel.
  2. Time travel is impossible because if it were possible we should have seen many time travelers by now, but nobody has encountered any time travelers.
  3. And time travel is impossible because, if there were time travel, then when time travelers go back and attempt to change history they must always botch their attempts to change anything, and it will appear to anyone watching them at the time as if nature is conspiring against them. Since observers have never witnessed this apparent conspiracy of nature, there is no time travel.
  4. If there were travel to the past along a closed timelike curve, then these events would occur before themselves and after themselves, but this violates our definition of the word “before.”
  5. Travel to the past is impossible because it allows the gaining of information for free. For example, print out this article that you are reading. Enter a time machine and go back to a time when you can give me the article before I have ever thought about time travel. I then publish it as this article in this encyclopedia. This all seems to be consistent with relativity theory, but who first came up with the information in this article? You had it before I did, but you obtained it from me.
  6. Probing the possibility of a contradiction in backwards time travel, the American philosopher John Earman has described a rocket ship that carries a very special time machine. The time machine is capable of firing a probe into its own past. Suppose the ship is programmed to fire the probe on a certain date unless a safety switch is on. Suppose the safety switch is programmed to be turned on if and only if the “return” or “impending arrival” of the probe is (or has been) detected by a sensing device on the ship. Does the probe get launched? It seems to be launched if and only if it is not launched. Is this like saying, “I’ll design a gun that shoots if and only if it doesn’t shoot”? Not quite. The way out of Earman’s paradox may require us to accept that (a) somehow people will be unable to build the probe or the safety switch or an effective sensing device, or (b) time travel probes must go so far back in time that they never survive and make it back to the time when they were launched, or (c) time travel into the past is impossible.

These complaints are a mixture of arguments that time travel is not logically possible, that it not physically possible, and that it is unlikely, given the empirical evidence. For more discussion of time travel, see the encyclopedia article “Time Travel.”

  1. Does Time Require Change? (Absolute vs. Relational Theories)

Absolute theories are theories that imply time exists independently of the spacetime relations exhibited by physical events (that is, changes). Relational theories imply time’s existence requires events. Some absolute theories describe spacetime as being like a container for events. The container exists with or without events in it. Relational theories imply there is no container without contents. John Norton’s metaphors might help. Our universe is like a painting, and absolute spacetime is like the painter’s canvas. If you take away the paint (the spacetime events) from the painting, you still have the canvas. Relational spacetime is like citizenship. Take away the citizens (the spacetime events), and you have no citizenship left.

Everyone agrees time cannot be measured without there being changes, but the present issue is whether it exists without changes. The absolute or substantival theories are theories that spacetime could exist even if there were no physical objects and events in the universe. Relational theories, on the other hand, imply that spacetime is nothing but the spatiotemporal relationships among possible objects and their possible events. Relational theories are also called “relationalist” theories.

There are two senses of “absolute” that need to be distinguished. As we are using the term, it means independent of the events. A second sense of “absolute” means independent of observer or reference frame. Einstein’s theory implies there is no absolute time in this second sense, yet it is an open question whether relativity theory rules out absolute theories in our first sense of the term. Although Aristotle accepted absolute time in the second sense, he rejected it in the first sense, and he adopted the classical relationalist position that, “neither does time exist without change.” [Physics, 218b]

However, the battle lines were most clearly drawn in the early 18th century when Leibniz argued for the relationalist position against Newton, who had adopted an absolute theory of time. Leibniz’s principal argument against Newton is a reductio ad absurdum. Suppose Newton’s absolute space and time were to exist. But one could then imagine a universe just like ours except with everything shifted five miles east and five minutes earlier. However, there would be no reason why this shifted universe does not exist and ours does. Now we have arrived at a contradiction because, if there is no reason for our universe over the shifted universe, then we have violated Leibniz’s Principle of Sufficient Reason: that there is an understandable reason for everything being the way it is. So, Newton’s absolute space and time do not exist. In short, the trouble with Newton’s absolutism is that it leads to too many unnecessary possibilities.

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

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

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

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

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

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

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

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