Time

clock2

Time has been studied by philosophers and scientists for 2,500 years,
and thanks to this attention it is much better understood today.
Nevertheless, many issues remain to be resolved. Here is a short list
of the most important ones—what time actually is; whether time exists
when nothing is changing; what kinds of time travel are possible; why
time has an arrow; whether the future and past are real; how to
analyze the metaphor of time's flow; whether future time will be
infinite; whether there was time before the Big Bang; whether tensed
or tenseless concepts are semantically basic; what is the proper
formalism or logic for capturing the special role that time plays in
reasoning; and what are the neural mechanisms that account for our
experience of time. Some of these issues will be resolved by
scientific advances alone, but others require philosophical analysis.

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

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

This article explores both what is now known about time and what is
controversial and unresolved, by addressing the questions listed in
the table of contents.

1. What Should a Philosophical Theory of Time Do?

Should it define the word "time"? Yes, but it is improper to demand
that we define our term "time" as a prelude to saying anything more
about time, in large part because, as we have learned more about time,
our definition has evolved. What we really want is to build a
comprehensive, philosophical theory of time that helps us understand
time by solving problems about time. We do not want to start building
this theory by adopting a definition of time that prejudices the
project from the beginning.

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

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

Another problem is to decide which of our intuitions about time should
be retained. Some of these intuitions may reflect deep insights into
the nature of time, and others may be faulty ideas inherited from our
predecessors. It is not obvious which is which. For one example, if we
have the intuition that time flows, but our science implies otherwise,
then which view should get priority? Philosophers of time must solve
the problem of how to treat our temporal intuitions.

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

A philosophical theory of time should describe the relationship
between instants and events. Does the instant that we label as "11:01
A.M." for a certain date exist independently of the events that occur
then? In other words, can time exist if no event is happening? This
question or problem raises the thorny metaphysical issue of 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 (cinema) shows a
film of cream being added into black coffee but runs the film
backwards, we in the audience can immediately tell that events could
not have occurred this way. We recognize the arrow of time because we
know about the one-directional processes in nature. This arrow or
unidirectionality becomes less and less apparent to us viewers as the
film subject gets smaller and smaller and the time interval gets
shorter and shorter until finally we are viewing processes that could
just as easily go the other way, at which point the arrow of time has
disappeared. Philosophers disagree about the explanation of the arrow.
Could it be a consequence of the laws of science? The arrow appears to
be very basic for understanding nature, yet it is odd that asymmetries
in time do not appear in the principal, basic dynamical laws of
physics. Could the arrow of time reverse some day? Philosophers wonder
what life would be like in some far off corner of the universe if the
arrow of time were reversed there. Would people there walk backwards
up steps while remembering the future?

Another philosophical problem about time concerns the two questions,
"What is the present, and why does it move into the past?" If we know
what the present is, then we ought to be able to answer the question,
"How long does the present last?" Regarding the "movement" of the
present into the past, many philosophers are suspicious of this notion
of the flow of time, the march of time. They doubt whether it is a
property of time as opposed to being some feature of human perception.
Assuming time does flow, is the flow regular? If the flow is
irregular, then perhaps Friday seconds last longer than Thursday
seconds, as the flow of Friday time slows to a crawl, or perhaps
Friday might contain more seconds than Thursday.

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

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

A full theory of time should address this constellation of
philosophical issues about time. Narrower theories of time will focus
on resolving a few members of this constellation, but the long-range
goal is to knit together these theories into a full, systematic,
detailed theory of time.
2. How is Time Related to Mind?

Physical time is public time, the time that clocks are designed to
measure. Psychological time or phenomenological time is private time.
It is perhaps best understood as awareness of physical time.
Psychological time passes swiftly for us while we are enjoying reading
a book, but it slows dramatically if we are waiting anxiously for the
water to boil on the stove. The slowness is probably due to focusing
our attention on short intervals of physical time. Meanwhile, the
clock by the stove is measuring physical time and is not affected by
anybody's awareness.

When a physicist defines speed to be the rate of change of position
with respect to time, the term "time" refers to physical time.
Physical time is more basic for helping us understand our shared
experiences in the world, and so it is more useful than psychological
time for doing science. But psychological time is vitally important
for understanding many human thought processes. We have an awareness
of the passage of time even during our sleep, and we awake knowing we
have slept for one night, not for one month. But if we have been under
a general anesthetic or have been knocked unconscious and then wake
up, we may have no sense of how long we have been unconscious.
Psychological time stopped. Some philosophers claim that psychological
time is completely transcended in the mental state called "nirvana."

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

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

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

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

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

At the end of the 18th century, Kant suggested a subtle relationship
between time and mind–that our mind actually structures our
perceptions so that we can know a priori that time is like a
mathematical line. Time is, on this theory, a form of conscious
experience, and our sense of time is a necessary condition of our
experience. In the 19th century, Ernst Mach claimed instead that our
sense of time is a simple sensation. This controversy took another
turn when other philosophers argued that both Kant and Mach were
incorrect because our sense of time is an intellectual construction
(see Whitrow, p. 64).

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

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

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

For more on the consciousness of time and related issues, see the
article "Phenomenology and Time-Consciousness."
3. What is Time?

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

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

A different, but popular answer to the question "What is time?" is
that time is the form of becoming. To assess this answer, which is
from Alfred North Whitehead, we need to be told what the term "form of
becoming" means; we need to be presented with a detailed theory of
time implying that time is the form of becoming; and we need to
investigate how it addresses those many features required for a
successful theory of time. A third answer or theory of time is Michael
Dummett's constructive model of time; he argues that time is a
composition of intervals rather than of durationless instants. The
model is constructive in the sense that it implies there do not exist
any times which are not detectable in principle by a physical process.
A fourth answer is that time is a distinguished one-dimensional
sub-space of spacetime, but spacetime is a substance. This
substantivalist answer is explored in a later section. There are many
other ways that our question has been answered.

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

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

Bothered by the contradictions they claimed to find in our concept of
time, some philosophers, notably Zeno, Plato, Spinoza, Hegel, and
McTaggart, answer the question, "What is time?" by replying that it is
nothing because it does not exist. In a similar vein, the early 20th
century English philosopher F. H. Bradley argues, "Time, like space,
has most evidently proved not to be real, but a contradictory
appearance….The problem of change defies solution." However, most
philosophers agree that time does exist. They just can not agree on
what it is.

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 are especially interested in time talk, in 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 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.

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

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

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

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

In the 18th century, Immanuel Kant said time and space are forms that
the mind projects upon the external things-in-themselves. He spoke of
our mind structuring our perceptions so that space always has a
Euclidean geometry, and time has the structure of the mathematical
line. Kant's idea that time is a form of apprehending phenomena is
probably best taken as suggesting that we have no direct perception of
time but only the ability to experience things and events in time.
Some historians distinguish perceptual space from physical space and
say that Kant was right about perceptual space. It is difficult,
though, to get a clear concept of perceptual space. If physical space
and perceptual space are the same thing, then Kant is claiming we know
a priori that physical space is Euclidean. With the discovery of
non-Euclidean geometries in the 1820s, and with increased doubt about
the reliability of Kant's method of transcendental proof, the view
that truths about space and time are 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
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, a little later 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, while sound waves rush out of your ear and converge on
the surface where the splash is unoccuring, and the pond is left
cooler at the temperature it was before the rock hit.] 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.

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.

With circular time, you can be assured that after your death you will
be reborn. The future will become 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 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 doesn't 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. The
logic of the term "time" that is embedded in our time talk may or may
not rule out a nonlinear structure for time, but there is no reason to
believe time is actually looped like this, nor that any object has
ever gone back in time.

Is time a basic concept, or does it depend on something more basic? 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?

4. What does Science Require of Time?
a. Relativity and Quantum Mechanics

The general theory of relativity and quantum mechanics are the two
most fundamental theories of physics, and the Big Bang theory is the
leading theory of cosmology. According to relativity and quantum
mechanics, spacetime is, loosely speaking, a collection of points
called "spacetime locations" where the universe's physical events
occur. Spacetime is four-dimensional and a continuum, and time is a
distinguished, one-dimensional sub-space of this continuum. Any
interval of time–any duration–is a linear continuum of instants. So, a
duration has a point-like structure similar to the structure of an
interval of real numbers; between any two instants there is another
instant, and there are no gaps in the sequence of instants. This is
what science requires time to be, but we haven't commented on why
science requires time to be this way.

This first response to the question "What does science require of
time?" is too simple. There are complications. There is an important
difference between the universe's cosmic time and a clock's proper
time; and there is an important difference between proper time and a
reference frame's coordinate time. Most spacetimes can not have
coordinate systems. Also, all physicists believe that relativity and
quantum mechanics are logically inconsistent and need to be replaced
by a theory of quantum gravity. A theory of quantum gravity is likely
to have radical implications for our understanding of time, such as
time and space being discrete rather than continuous.

Aristotle, Leibniz, Newton, and everyone else before Einstein,
believed there was a frame-independent duration between two events.
For example, if the time interval between two lightning flashes is 100
seconds on someone's accurate clock, then the interval also is 100
seconds on your own accurate clock, even if you are flying by at an
incredible speed. Einstein rejected this piece of common sense in his
1905 special theory of relativity when he declared that the time
interval 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.

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 either time or space
alone. 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. What
does not vary is their union, what we now call "spacetime." It seems
to follow that the division of events into the past ones, the present
ones, and the future ones is also not "independently real." However,
space and time are not completely equivalent even in relativity theory
because time is a "distinguished" sub-space of the 4-d spacetime
continuum. Being distinguished implies that time is a special
dimension unlike the space dimensions, even when we confine our
attention to a single reference frame. For example, a person can move
easily forward and backward in any spatial dimension, but not in the
time dimension.

A coordinate system or reference frame is a way of representing space
and time using numbers to represent spacetime points. Science
confidently 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 in any reference
frame are real numbers, not merely rational numbers. Each number
designates an instant of time, and time is a linear continuum of these
instants ordered by the happens-before relation, similar to the
mathematician's line segment that is ordered by the less-than
relation. Therefore, if these fundamental theories are correct, then
physical time is one-dimensional rather than two-dimensional, and
continuous rather than discrete. These features do not require time to
be linear, however, because a segment of a circle is also a linear
continuum, but there is no evidence for circular time, that is, for
causal loops. Causal loops are worldlines that are closed curves in
spacetime.

What about instants? A duration is an ordered set of instants, not a
sum of instants. That is, instants are members of durations, not parts
of them. Any duration is infinitely divisible, and it endlessly
divides into more intervals; it never divides into instants. The parts
of durations are just more durations. Instants are like real numbers
in that they are boundaries of durations. They are locations in time,
but they are "in" time as members are in sets, not as parts are in
wholes.

The ordering of instants by the happens-before relation, that is, by
temporal precedence, is complete; there are no gaps in the sequence of
instants. Knowing an object, such as an interval of time, is
infinitely divisible does not tell you how many elements or ultimate
parts it has, other than that there are infinitely many. It might have
aleph zero or aleph one elements. No physical object is infinitely
divisible; and the reason is that it can be divided into only a finite
number of quarks and electrons and other particles. However, it is
often convenient for certain mathematical operations to treat physical
objects as if they were infinitely divisible. Physical space and
physical time are generally believed to be infinitely divisible.
Regarding the number of instants in any (non-zero) duration, time's
being a linear continuum implies the ordered instants are so densely
packed that between any two there is a third, so that no instant has a
next instant. In fact, time's being a linear continuum implies that
there is a nondenumerable infinity of instants between any two
instants, that is, an aleph one number of instants. 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 here is that, although time is
not quantized in quantum theory, for times shorter than about 10-43
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 of saying the reals can be embedded into an
interval of instants 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 do not 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 an alternative to string
theory, loop quantum gravity, does not. (See "Atoms of time.")

Relativity theory challenges a great many of our intuitive beliefs
about time. The theory is inconsistent with the common sense belief
that the temporal order in which two events occur is independent of
the observer's point of reference. For events occurring at the same
place, relativity theory implies the order is absolute (independent of
the frame) and so agrees with common sense, 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 simultaneously with B in yet another
frame.

Science impacts our understanding of time in other fundamental ways.
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 by
arguing that, if motion is relative, then we could call the speeding
twin "stationary" and it would follow that this twin is now the one
who ages more rapidly. This argument is called the twins paradox of
special relativity. Experts now are agreed that the mistake is within
the argument for the paradox, not within relativity theory. The twins
feel different accelerations, so their motion is not completely
symmetric. As is shown in more detail in the Supplement of Frequently
Asked Questions, the argument fails to notice the radically different
relationships that each twin has to the rest of the universe as a
whole. This is why one twin's proper time is different than the
other's.

[An object's proper time along its worldline, that is, along its path
in 4-d spacetime, is the time elapsed by a clock having the same
worldline. Coordinate time is the time measured by a clock at rest in
the (inertial) frame. A clock isn't really measuring the time in a
reference frame other than one fixed to the clock. In other words, a
clock primarily measures the elapsed proper time between events that
occur along its own worldline. Technically, a clock is a device that
measures the spacetime interval along its own worldline. If the clock
is at rest in an inertial frame, then it measures the "coordinate
time." If the spacetime has no inertial frame then it can't have a
coordinate time.]

There are two kinds of time dilation. Special relativity's time
dilation involves speed; general relativity's also involves
acceleration and gravitational fields. Two ideally synchronized clocks
need not stay in synchrony if they undergo different accelerations or
different gravitational forces. This gravitational time dilation 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. Every black hole brings an end to time inside itself.
If, as many physicists suspect, the microstructure of spacetime (near
the Planck length which is much smaller than the diameter of a proton)
is a quantum foam of changing curvature of spacetime with black holes
forming and dissolving, then time loses its meaning at this small
scale. The philosophical implication is that time exists only when we
are speaking of regions large compared to the Planck length. [If loop
quantum gravity turns out to be the theory that unites quantum
mechanics and relativity, then black holes do not have infinite
densities at their center, and light would be trapped inside only for
a finite period, after which what has fallen into the hole will be
ejected.]

General Relativity theory may have even more profound implications for
time. In 1948, the logician Kurt discovered radical solutions to
Einstein's equations, solutions in which there are closed timelike
curves, so that as one progresses forward in time along one of these
curves one arrives back at one's starting point. Gödel drew the
conclusion that if matter is distributed so that there is Gödelian
spacetime (that is, with a preponderance of galaxies rotating in one
direction rather than another), then the universe has no linear time.
b. The Big Bang

The Big Bang is a violent explosion of spacetime that began billions
of years ago. It is not an explosion in spacetime. The Big Bang theory
in some form or other is accepted by the vast majority of astronomers,
but it is not as firmly accepted as is the theory of relativity. Here
is a quick story of its origin. In 1922, the Russian physicist
Alexander Friedmann predicted from general relativity that the
universe should be expanding. In 1927, the Belgian physicist Georges
Lemaitre suggested that galaxy movement could best be accounted for by
this expansion. And in 1929, the American astronomer Edwin Hubble made
careful observations of clusters of galaxies and confirmed that they
are undergoing a universal expansion, on average.

Atoms are not expanding; our solar system is not expanding; even the
cluster of galaxies to which the Milky Way belongs is not expanding.
But most every galaxy cluster is moving away from the others. It is as
if the clusters are exploding away from each other, and in the future
they will be very much farther away from each other. Now, consider the
past instead of the future. 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 the universe was in a state of
nearly 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, and so it begin
expanding when it was extremely hot. Presently the average temperature
of space in all very large regions is 2.7 degrees Celsius above
absolute zero. The Big Bang theory is a theory of how our universe
evolved, how it expanded and cooled from this beginning. This
beginning process is called the "Big Bang."

As far as we knew back in the 20th century, the entire universe was
created in the Big Bang, and time itself came into existence "at that
time." So, asking what happened before the Big Bang was properly taken
to be like asking what on Earth is north of the North Pole. With the
appearance of the new theories of quantum gravity and the cosmic
landscape in the 21st century, the question has been resurrected as
legitimate.

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 is 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 rather than closed at t = 0.
Looking back to the Big Bang is then like following the positive real
numbers back to ever smaller positive 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 in
order to simplify the discussion ahead, this article will speak of
"the" Big Bang event as if it were a single origin event.

There are serious difficulties in defending the Big Bang theory's
implications about the universe's beginning and its future. Classical
Big Bang theory is 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 10-43 seconds after "the" Big Bang
event. Therefore, current science cannot speak with confidence about
the nature of time within the Planck era. If a theory of quantum
gravity does get confirmed, it should provide information about this
Planck era, and it may even allow physicists to answer the question,
"What caused the Big Bang?"

The scientifically radical, but theologically popular, answer, "God
caused the Big Bang, but He, himself, does not exist in time" is a
cryptic answer 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 their God is usually stronger
than belief in any scientific hypothesis, or in any epistemological
desire for a scientific justification of their remark about God, or in
the importance of satisfying any philosopher's demand for
clarification.

Some physicists are advocating revision of the classical Big Bang
theory in order to allow for the "cosmic landscape" or "multiverse,"
in which there are multiple Big Bangs in parallel universes and an
infinite amount of time before our Big Bang. See (Veneziano, 2006). In
some of these universes there is no time dimension. However, this new
theory is not generally accepted by theoretical cosmologists.
c. Infinite Time

There are three ways to interpret the question of whether physical
time is infinite: (a) Was there an infinite amount of time in the
universe's past? (b) Is time infinitely divisible? (c) Will there be
an infinite amount of time in the future?

(a) Was there an infinite amount of time in the past? Aristotle argued
"yes," but by invoking the radical notion that God is "outside of
time," St. Augustine declared, "Time itself being part of God's
creation, there was simply no before!" (that is, no time before God
created everything else but Himself). So, for theological reasons,
Augustine declared time had a finite past. After advances in astronomy
in the late 19th and early 20th centuries, the question of the age of
the universe became a scientific question. With the acceptance of the
classical Big Bang theory, the amount of past time was judged to be
less than 14 billion years because this is when the Big Bang began.
The assumption is that time does not exist independently of the
spacetime relations exhibited by physical events. Recently, however,
the classical Big Bang theory has been challenged. There could be an
infinite amount of time in the past according to some proposed, but as
yet untested, theories of quantum gravity based on the assumptions
that general relativity theory fails to hold for infinitesimal
volumes. These theories imply that the beginning of the Big Bang was
actually an expansion from a pre-existing physical state. There was
never a singularity. In that case our Big Bang could be just one bang
among other bangs throughout an infinite past of the landscape. For a
discussion of these controversial theories requiring an infinite past
time, see (Veneziano, 2006).

(b) Is time infinitely divisible? Yes, because general relativity and
quantum mechanics require time to be a continuum. But the answer is no
if these theories are eventually replaced by a relativistic quantum
mechanics that quantizes time. "Although there have been suggestions
that spacetime may have a discrete structure," Stephen Hawking said in
1996, "I see no reason to abandon the continuum theories that have
been so successful."

(c) Will there be an infinite amount of time in the future? Probably.
According to the classical theory of the Big Bang, the answer depends
on whether events will keep occurring. The best estimate from the
cosmologists these days is that the expansion of the universe is
accelerating and will continue forever. There always will be the
events of galaxy clusters getting farther apart, and so future time
will have an infinite duration, even though gravity will continue to
compact much of the matter into black holes.

There have been interesting speculations on how conscious life could
continue forever, despite the fact that the available energy for life
will decrease as the universe expands, and despite the fact that any
life swept up into a black hole will reach the center of the hole in a
finite time at which point death will be certain. For an introduction
to these speculations, see (Krauss and Starkman, 2002).
d. Atoms of Time

In the classical theories of relativity and quantum mechanics, time is
not quantized, but is a continuum having the character described
above. However, if certain, as yet untested, theories attempting to
unify relativity and quantum mechanics are correct–such as the theory
of loop quantum gravity–then time is composed of discrete durations
lasting about 10-43 second. There is a shortest duration for any
possible event, and time is digital rather than analog.
5. What Kinds of Time Travel are Possible?

Most philosophers believe time travel is possible. In time travel, the
traveler's journey, as judged by the traveler, takes a different
amount of time than the journey does as judged by those who do not
take the journey. That is, there is a difference, and not merely a
verbal disagreement, between the traveler's inner time or proper time
and the external or coordinate time of those who do not take the
journey. However, physically realistic time travel does not allow this
external time lapse to be zero; there is no "poofing" into the past or
"poofing" into the future in the way we read about time travel in many
science fiction stories.

According to relativity theory, there are two ways to travel into
another person's future: by moving at high speed or by taking
advantage of an intense gravitational field. If you have a fast enough
spaceship, you can travel to the year 4,500 A.D. on Earth. You can
affect that future, not just view it. But you can not get back to your
earlier time by reversing your velocity or reversing the gravitational
field. Also, your travel is to someone else's future, not your own.
You are always in your own present in these kinds of time travel to
the future.

But relativity theory also allows a much stranger kind of time travel,
travel to your own past. For example, 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 your own 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.
Relativity theory even permits you to travel back and meet yourself as
a child. But, although you can meet yourself, 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.

There are several well known arguments against the physical
possibility of certain kinds of time travel to the past. Despite the
controversy, none are generally considered to be decisive. (1) Time
travel is impossible, some say, because if it were possible we should
have seen many time travelers by now, but nobody has encountered any
time travelers. (2) And time travel is impossible because, if there
were time travel, then when time travelers go back and attempt to
change history they must always botch their attempts to change
anything, and it will appear to the rest of us at the time as if
nature is conspiring against them. Since we have never witnessed this
apparent conspiracy of nature, there is no time travel. (3) A third
argument for the impossibility of time travel is that 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 word "before," or violates our concept of time, so
this odd solution of Einstein's equations is not a physically
realistic solution. (4) Travel to the past is impossible because it
allows the gaining of information for free. For example, print out
this article that you are reading. Enter a time machine with it. Give
me the article before I ever thought about time travel. I then publish
it in this encyclopedia. This all seems to be consistent with
relativity theory, but who first came up with the information in this
article? You had it before I did, but you obtained it from me. (5)
Probing the possibility of a contradiction in backwards time travel,
the American philosopher John Earman has described a rocket ship that
carries a very special time machine. The time machine is capable of
firing a probe into its own past. Suppose the ship is programmed to
fire the probe on a certain date unless a safety switch is on. Suppose
the safety switch is programmed to be turned on if and only if the
"return" or "impending arrival" of the probe is (or has been) detected
by a sensing device on the ship. Does the probe get launched? It is
launched if and only if it is not 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 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.

For more discussion of time travel, see the encyclopedia article "Time Travel."
6. Is the Relational Theory Preferable to the Absolute Theory?

Absolute theories are theories that imply time exists independently of
the spacetime relations exhibited by physical events. Relational
theories imply it does not. 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 objects
and changes, but the present issue is whether it exists without
objects and changes. The absolute or substantival theories are
theories 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 objects and their events, so that spacetime
reduces to sets of possible spatiotemporal relations.

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. Aristotle accepted absolute time in this second sense, but he
rejected it in our sense of being independent of events and took the
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 glove versus a left 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's view of the 19th century that, if you hold the bucket
still but spin the background stars, the water will creep up the side
of the bucket. 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,
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?
7. Does Time Flow?

"It is as if we were floating on a river, carried by the current past
the manifold of events which is spread out timelessly on the bank,"
said one philosopher trying to capture time's flow with a helpful
metaphor. Santayana offered another: "The essence of nowness runs like
fire along the fuse of time." The philosopher's goal is to clarify the
idea of time's flow, the passage of time. Everyone agrees that the
passage of time "appears" to us humans to flow, although few
scientists or philosophers believe that all conscious beings recognize
the flow; hawks do not, although they are apt at spotting the
movements of their prey. Even if time does flow, there is the
additional question of whether the flow can change. Can physical
time's flow be slower on Friday afternoon, compared to Monday morning?

There are two categories of theories of time's flow. The first, and
most popular among physicists, is that the flow is an illusion, the
product of a faulty metaphor. Time exists, things change, but time
does not flow objectively, although there may well be some objective
feature of our brains that causes us to believe we are experiencing a
flow of time; but in that case time flows only in a subjective sense
of the term. The theory is sometimes characterized as a
"myth-of-passage" theory. As we shall see, this theory of time's flow
is normally the one adopted by those who believe McTaggart's B-series
is more fundamental than his A-series.

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

Some dynamic theories imply that the flow is a matter of events
changing from being indeterminate in the future to being determinate
in the present and past. Time's flow is really events becoming
determinate. Thus dynamic theorists speak of time's flow as "temporal
becoming." Another dynamic theory implies that the flow is a matter of
events changing from being future, to being present, to being past.
This is the kind of flow associated with McTaggart's A-series of
events.

Opponents of dynamic theories complain that when events change in
these senses, the change is not a real change in the event's
essential, intrinsic properties, but only in the event's relationship
to the observer. For example, saying the death of Queen Anne is an
event that changes from present to past is no more of a real change in
the event than saying her death changed from being approved of to
being disapproved of. This extrinsic change in approval does not count
as a real change in her death, and neither does the so-called change
from present to past. Attacking the notion of time's flow in this
manner, Grünbaum said: "Events simply are or occur…but they do not
'advance' into a pre-existing frame called 'time.' …[T]ime is a system
of relations between events, and as events are, so are their
relations. An event does not move and neither do any of its
relations." So, Grünbaum denies the objective nature of McTaggart's
A-series and points out that the flow of time is an illusion or myth.

Instead of arguing that events change their properties, some advocates
of the dynamic theory of time embrace the flow of time by saying that
the flow is reflected in the change over time of truth values of a
sentence or proposition. For example, the sentence "It is now raining"
was true during the rain yesterday but has changed to false on today's
sunny day. It is these sorts of truth value changes that are at the
root of time's flow. In response, critics suggest that the indexical
(or token reflexive) sentence "It is now raining" has no truth value
because the reference of "now" is unspecified. If it can not have a
truth value, it can not change its truth value. However, the sentence
is related to a sentence that does have a truth value. Supposing it is
now midnight here on April 1, 2007 in Sacramento, California, then the
indexical sentence "It is now raining" is related to the complete or
context-explicit sentence "It is raining at midnight on April 1, 2007
in Sacramento." Only these non-indexical, non-context-dependent,
complete sentences have truth values, and these truth values do not
change with time. So, events do not change their properties because
complete sentences do not change their truth values.

Other advocates of the dynamic theory of time ask us to analyze time's
flow in terms of facts that come into existence. This coming into
existence of facts, the actualization of new states of affairs, is
time's flow.

Tim Maudlin argues for a version of the dynamic theory that is very
different than all of the above. He argues that the objective flow of
time is fundamental and unanalyzable; it is a fundamental, irreducible
fact that time passes, and this passage just is the flow of time. He
is happy to say "time does indeed pass at the rate of one hour per
hour" (Maudlin, 2007, p. 112), although other philosophers have called
this rate "meaningless." Maudlin also is an advocate of the block
universe theory and believes the passage of time is an ingredient of
this single block entity.

Regardless of how the metaphor of time's flow is analyzed, or even if
it is taken as fundamentally unanalyzable, the passage of time implies
a direction of time.
8. What Gives Time its Direction or "Arrow"?
a. What Needs to be Explained

The arrow of time is what distinguishes a group of events ordered by
the happens-before relation from those ordered by its converse, the
happens-after relation. Time's arrow is evident in the process of
mixing cool cream into hot coffee. You soon get lukewarm coffee, but
you never notice the reverse–lukewarm coffee separating into a cool
part and a hot part. Such is the way this irreversible thermodynamic
process goes. Time's arrow is also evident when you prick a balloon.
The air inside the balloon rushes out; it never stays in the balloon
as it was before the pricking. So, the pricking starts an irreversible
process. The arrow of a physical process is the way it normally goes,
the way it normally unfolds through time. If a process goes only
one-way, we call it an "irreversible process." (Strictly speaking, a
reversible process is one that is reversed by an infinitesimal change
of its surrounding conditions, but we can overlook this fine point
because of the general level of the present discussion.) The
amalgamation of the universe's irreversible processes produces the
cosmic arrow of time, the master arrow. Usually this arrow is what is
meant when one speaks simply of "time's arrow." By convention, we say
the arrow is directed toward the future.

There are many goals for a fully developed theory of time's arrow. It
should tell us (1) why this arrow exists; (2) why the arrow is
apparent in macro processes but not micro processes; (3) what it would
be like for the arrow to reverse direction; (4) what the relationships
are among the various more specific arrows of time–the various
temporally asymmetric processes such as entropy increases [the
thermodynamic arrow], causes preceding their effects [the causal
arrow], light radiating from its source rather than converging into it
[the electromagnetic arrow], and our knowing the past more easily than
the future [the knowledge arrow]; and (5) what are the characteristics
of a physical theory that pick out a preferred direction in time.

Because the physical processes we commonly observe do have an arrow,
you might think that an inspection of the basic physical laws would
readily reveal time's arrow. It will not. With very minor exceptions,
all the basic laws of fundamental processes are time symmetric. (It is
assumed here that the second law of thermodynamics is not basic but
somehow derived.) This means, according to a principal definition of
time symmetry, that if a certain process is allowed by the laws, then
that process reversed in time is also allowed, and either direction is
as probable as the other. Maxwell's equations of electromagnetism, for
example, can be used to predict that television signals can exist, but
the equations do not tell us whether those signals arrive before or
arrive after they are transmitted. In other words, these basic laws of
science do not imply an arrow of time.

Suppose you have a movie of a basic physical process such as two
electrons bouncing off each other. You can not actually create this
movie because the phenomenon is too small, but 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 basic laws of science, and they would be equally
probable processes. You could not tell from just looking at the movie
whether you were looking at the original or at it being shown
backwards in time. So, time's arrow is not revealed in this
microscopic process.

The "disappearance" of time's arrow in microscopic process, does not
show that time itself fades away as you look at briefer and smaller
processes; this is because there are still events happening, and so
time still exists there. Also, it is important to note that, although
it is interesting to explain how we humans are able to detect the
arrow, the more challenging philosophical question is to explain why
time has an arrow.
b. Explanations or Theories of the Arrow

In the 19th century, the new kinetic theory of gases was supposed to
provide the foundation for all gas behavior, yet this foundational
theory is time symmetric. That is, the theory is insensitive to the
arrow of time, to the distinction between past and future–because a
moving molecule could just as well move in one direction as in the
reverse direction. How were the physicists to resolve this apparent
contradiction of having a temporally symmetric theory at the
foundation of a theory that is supposed to account for irreversible
gas processes such as the escape of gas from a balloon pricked with a
pin? The first clue was discovered in the mid-19th century by the
German physicist Rudolf Clausius. He devised an early version of the
2nd law of thermodynamics, which, speaking informally, is the claim
that a isolated system will evolve to be more disordered or complex,
with some of its useful energy converting to heat. [A isolated system
is a system left to itself; it is a region isolated from outside
influences, a region where energy can not come in or go out.] That is,

(a) 2nd Law: In an isolated system, entropy never decreases.

Entropy is Clausius's word for the measure of this disorder; it
measures the conversion of useful to "useless" energy by irreversible
processes. As R. A. Fisher expressed it, entropy changes lead to a
progressive disorganization of the physical world, at least from the
human standpoint of the utilization of energy. As time goes on, some
sub-systems do become progressively more organized, such as when we
build a house on a bare lot, but this organization is at the expense
of a greater degree of disorganization elsewhere such as the depletion
of natural resources and the digestion of food by the house builders
and, ultimately, the degradation of the sun.

It seemed to many physicists, beginning with Ernst Mach, that time's
arrow–in all processes and not just in gas behavior–is reducible to or
grounded in entropy increase. This implies that in a universe in
maximum equilibrium where entropy changes are absent, there will not
be an arrow of time. This entropy theory of time's arrow implies that
our having traces of the past but not of the future reduces to entropy
increases, as does our inclination to say causes happen before their
effects rather than after.

Another deep question is, "Why should there be more disorder in the
future?" The Austrian physicist Ludwig Boltzmann had an answer in
1872. Boltzmann claimed that it is a matter of probability because,
for complex systems, that is, systems with many particles, disordered
states of the system are more probable than ordered states. There are
many more microstates in which, from a macro perspective, the system
is disordered than microstates in which the system is ordered, so it
is very probable that the system will naturally end up in the most
generic possible macrostate. Boltzmann redefined the concept of
entropy in terms of the statistics of molecular motion, and he deduced
a revised 2nd law from probability theory:

(b) 2nd Law: In an isolated system, entropy is likely not to decrease.

His treatment of entropy as being basically a statistical concept was
broadly accepted, as was Mach's and his claim that time's arrow is to
be explained in terms of entropy increase.

Boltzmann's achievement soon had to confront two obstacles, one from
Henri Poincaré and one from Josef Loschmidt. First, Poincaré. 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 molecules in a cup of coffee. Poincaré'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 coffee will separate into hot
coffee and cool cream. This reversal would be expected to take 10N
seconds, where N is the number of molecules involved. The number is
staggering, but still finite; so, strictly speaking, there are no
irreversible processes and no long term entropy increase. Whenever
entropy rises it will eventually fall. That implies there is an
apparent contradiction between Poincaré's theorem and Boltzmann's.

To avoid this Poincaré problem, physicists redefined the second law:

(c) 2nd Law: In an isolated system, entropy is likely not to
decrease for any period of time that is short compared to the Poincaré
period for that system.

Josef Loschmidt pointed out another problem with Boltzmann's approach
to the arrow of time. Loschmidt realized that Boltzmann's statistical
mechanics predicts for any point in time not only that entropy should
be higher in the future but also that it should be higher in the past.
However, we know that it was not higher in the past. Here is a graph
representing this knowledge.

entropy

The conclusion to be drawn from this is that entropy increase is only
part of the story of time's cosmic arrow.

Loschmidt suggested that the low entropy in the past must be explained
by what the initial conditions happened to be like at the beginning of
the universe. Boltzmann agreed. Among cosmologists, this is now the
generally accepted answer to the origin of time's arrow.

Yet this answer leads naturally to the request for an explanation of
the initial configuration of our universe. Is this temporally
asymmetric initial boundary condition simply a brute fact, as many
physicists believe, or are there as yet undiscovered laws to explain
the fact, as many other physicists believe–either to explain it as
necessarily having had to happen or to explain it as having been
highly probable? Objecting to inexplicable initial facts as being
unacceptably ad hoc, the Swiss physicist Walther Ritz and, more
recently, Roger Penrose, say we must not yet have found the true laws
(or invented the best laws) underlying nature's behavior. We need to
keep looking for basic, time asymmetrical laws in order to account the
initial low entropy and thus for time's arrow.

The low entropy appears to be due to the microscopic Big Bang region
having just the right amount of homogeneity or smoothness so that
galaxies would eventually form. If it were intially smoother, then
there would be no congealing of matter into galaxies; if it were
intially less smooth, then most all the matter would have long ago
ended up in large black holes. So, the issue of how to explain the
thermodynamic arrow is the issue of why the Big Bang region had just
the right smoothness.
c. Multiple Arrows

Consider the difference between time's arrow and time's arrows. The
direction of entropy change is the thermodynamic arrow. Here are some
suggestions for additional arrows:

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

Most physicists suspect all these arrows are linked so that we can not
have some arrows reversing while others do not. For example, the
collapse of the wave function is generally considered to be due to an
increase in the entropy of the universe. However, the linkage of all
the arrows may require as yet undiscovered laws.
d. Reversing Time

But could all the arrows have pointed the other way? That is, could
the cosmic arrow of time have gone the other way? Most physicists
suspect that the answer is yes, and it would have gone the other way
if the initial conditions of the universe at the Big Bang had been
different.

Should we also expect that at some time in the future all the arrows
will reverse? Unfortunately, it is still an open question in
philosophy as to what it means for time's arrow to reverse. For a
technical introduction to the debate, see Savitt, pp. 12-19.

Supposing the cosmic arrow of time were to reverse, it would be
possible for our past to be re-created and lived in reverse order.
This re-occurrence of the past is different than the re-living of past
events via time travel. With cyclical time or with time travel in a
causal loop, the past is re-visited in the original order that the
past events occurred; the past is not visited in reverse order.

Philosophers have gone on to ask other interesting questions about
different scenarios involving the reversal of time's arrow. Suppose
the cosmic arrow of time were someday to reverse in a distant,
populated region far away from Earth. Imagine what life would be like
for the time-reversed people. First off, would it be possible for them
to be conscious? Assuming consciousness is caused by brain processes,
could there be consciousness if their nerve pulses reversed, or would
this reversal destroy consciousness? This is a difficult question, but
supposing the answer is that they would be conscious, and supposing
that anyone's future is what will happen, not what has happened, then
what would their experience be like? It has been suggested that if we
were able to watch them in their region of space, they would appear to
us to be pre-cognitive. Could they use this to win gambling bets on,
say, the roll of the dice? Probably not, say other philosophers who
argue that the inner experience of time-reversed people must be no
different than ours.

If Aristotle were correct that the future, unlike the past, is
undetermined or open, then the future of people in the time-reversed
region would be open, too. But it is like our past. What can we
conclude from this? Do we conclude that our past might really be
undetermined and open, too? That our past could change?

And there are other questions. Consider communication between the two
regions. If we sent a signal to the time-reversed region, could our
message cross the border, or would it dissolve there, or would it
bounce back? If they successfully sent a recorded film across the
border to us, should we play it in the ordinary way or in reverse? If
the arrow of time were to reverse in some region, would not dead
people in that region become undead, but is that metaphysically
possible?
9. Is Only the Present Real?

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

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

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

The presentist and the advocate of the growing past will usually unite
in opposition to the block universe (eternalism) on the grounds that
it misses the special "open" character of the future and the equally
significant point that the present is so much more vivid to a
conscious being than is any other time-slice of spacetime. The
advocates of the block universe counter that only the block universe
can make sense of relativity's implication that, if people are in
certain relative motions, an event in person A's present can be in
person B's future. Presentism and the growing-past theories must
suppose that this event is both real and unreal because it is real for
A but not real for B. Surely that conclusion is unacceptable, they
claim. Their two key assumptions here are that relativity does provide
an accurate account of the spatiotemporal relations among events, and
that if there is some frame of reference in which two events are
simultaneous, then if one of the events is real, so is the other.

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

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

Many philosophers, however, do not agree with Einstein.

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

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

The principal motive for adopting the Aristotelian position arises
from the belief that if sentences about future human actions are now
true, then humans are fated (or 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, and it
faces a series of challenges. First, if there really is no free will,
or if free will is compatible with fatalism (or determinism), then the
motivation to deny truth values to predictions is undermined.

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

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

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

There will be a sea battle tomorrow.

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

So, we should wake up the admiral.

Without the premises in this argument having truth values, that is,
being true or false, we cannot properly assess the argument using the
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, so Aristotle's position is
implausible.

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

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

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

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

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

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

Custer died in Montana.

If we apply the Correspondence Theory directly to this sentence, 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. One approach, the classical tenseless
approach, argues that the Correspondence Theory should be applied only
to the result of analyzing away tensed sentences into equivalent
sentences that do not use tenses. They might say that the sentence
"Custer died in Montana" has this equivalent "eternal" sentence:

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

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

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

This analysis of tenses without appeal to tensed facts is challenged
on the grounds that it can succeed only for utterances or
inscriptions, but a sentence can be true even if never uttered or
written by anyone. There are other challenges. Roderick Chisholm and
A. N. Prior claim that the "is" in the sentence "It is now midnight"
is essentially present tensed because there is no translation using
only tenseless verbs. Trying to analyze it as, say, "There is a time t
such that t = midnight" is to miss the essential reference to the
present in the original sentence. The latter sentence is always true,
but the original is not, so the tenseless analysis fails. There is no
escape by adding "and t is now" because this last indexical still
needs analysis, and we are starting a vicious regress.

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, and science
fails to do this because it does not recognize them as being real
facts. Science, they say, 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.

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

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

D. H. Mellor, who advocates a newer subjective theory of tenses, says
there's no mystery about the meaing of tensed sentences that requires
tensed facts or tensed properties. More specifically, he argues that
the truth conditions of any tensed sentence can be explained without
tensed facts even if Chisholm and Prior are correct that some tensed
sentences can not be translated into tenseless ones. Mellor would say
it is not the pastness of the painful event that explains why I say,
"Thank goodness that's over." My gladness is explained by my belief
that the event is past, plus its being true that the event is past. In
addition, tenseless sentences can be used to explain the logical
relations between tensed sentences: that one tensed sentence implies
another, is inconsistent with yet another, and so forth. And
understanding truth conditions and truth implications is the main
thing you know when you understand a declarative sentence. In other
words, the meaning of tensed sentences can be explained without
utilizing tensed properties or tensed facts. Then Ockham's Razor is
applied. If we can do without essentially tensed facts, then we should
say essentially tensed facts do not exist. To summarize, tensed facts
were presumed to be needed to account for the truth of tensed talk;
but the analysis shows that ordinary tenseless facts are adequate. So,
there are no essentially tensed facts, according to Mellor.
11. What is Temporal Logic?

Temporal logic is the representation of information about time by
using the methods of symbolic logic. The classical approach to
temporal logic is via tense logic, a formalism that adds tense
operators to an existing system of symbolic logic. The pioneer in the
late 1950s was A. N. Prior. He created a new symbolic logic to
describe our use of time words such as "now," "happens before,"
"afterwards," "always," and "sometimes". The relationships that
propositions have to the past, present, and future help to determine
their truth-value. A proposition, such as "Socrates is sitting down"
is allowed to be true at one time and false at another time.

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

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

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

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

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

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

Occasionally the method of temporal arguments uses a special constant
symbol, say "n", to denote now, the present time. This helps with the
translation of common temporal statements. For example, the statement
that Q has always been true may be translated into first-order
temporal logic as

(∀t)[(t < n) → Q(t)].

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

The following questions are addressed in the Time Supplement article:

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

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

* What are Proper Times, Coordinate Systems, and Lorentz Transformations?

13. References and Further Reading

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