Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology, epistemology, and character of space and time.
While such ideas have been central to philosophy from its inception,
the philosophy of space and time was both an inspiration for and a
central aspect of early analytic philosophy.
The subject focuses on a number of basic issues, including whether time
and space exist independently of the mind, whether they exist
independently of one another, what accounts for time's apparently
unidirectional flow, whether times other than the present moment exist,
and questions about the nature of identity (particularly the nature of
identity over time).
Ancient and medieval views
The earliest recorded Western philosophy of time was expounded by the ancient Egyptian thinker Ptahhotep (c. 2650–2600 BC) who said:
Follow your desire as long as you live, and do not perform more than is ordered, do not lessen the time of following desire, for the wasting of time is an abomination to the spirit...
— 11th maxim of Ptahhotep
The Vedas, the earliest texts on Indian philosophy and Hindu philosophy, dating back to the late 2nd millennium BC, describe ancient Hindu cosmology, in which the universe goes through repeated cycles of creation, destruction, and rebirth, with each cycle lasting 4,320,000 years. Ancient Greek philosophers, including Parmenides and Heraclitus, wrote essays on the nature of time.
Plato, in the Timaeus, identified time with the period of motion of the heavenly bodies, and space as that in which things come to be. Aristotle, in Book IV of his Physics,
defined time as the number of changes with respect to before and after,
and the place of an object as the innermost motionless boundary of that
which surrounds it.
In Book 11 of St. Augustine's Confessions,
he ruminates on the nature of time, asking, "What then is time? If no
one asks me, I know: if I wish to explain it to one that asketh, I know
not." He goes on to comment on the difficulty of thinking about time,
pointing out the inaccuracy of common speech: "For but few things are
there of which we speak properly; of most things we speak improperly,
still the things intended are understood."
But Augustine presented the first philosophical argument for the
reality of Creation (against Aristotle) in the context of his discussion
of time, saying that knowledge of time depends on the knowledge of the
movement of things, and therefore time cannot be where there are no
creatures to measure its passing (Confessions Book XI ¶30; City of God Book XI ch.6).
In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning, medieval philosophers and theologians developed the concept of the universe having a finite past with a beginning, now known as Temporal finitism. The Christian philosopher John Philoponus
presented early arguments, adopted by later Christian philosophers and
theologians of the form "argument from the impossibility of the
existence of an actual infinite", which states:
- "An actual infinite cannot exist."
- "An infinite temporal regress of events is an actual infinite."
- "∴ An infinite temporal regress of events cannot exist."
In the early 11th century, the Muslim physicist Ibn al-Haytham (Alhacen or Alhazen) discussed space perception and its epistemological implications in his Book of Optics (1021). He also rejected Aristotle's definition of topos (Physics IV) by way of geometric demonstrations and defined place as a mathematical spatial extension. His experimental proof of the intro-mission model of vision led to changes in the understanding of the visual perception of space, contrary to the previous emission theory of vision supported by Euclid and Ptolemy.
In "tying the visual perception of space to prior bodily experience,
Alhacen unequivocally rejected the intuitiveness of spatial perception
and, therefore, the autonomy of vision. Without tangible notions of
distance and size for correlation, sight can tell us next to nothing
about such things."
Realism and anti-realism
A traditional realist position in ontology is that time and space have existence apart from the human mind. Idealists, by contrast, deny or doubt the existence of objects independent of the mind. Some anti-realists,
whose ontological position is that objects outside the mind do exist,
nevertheless doubt the independent existence of time and space.
In 1781, Immanuel Kant published the Critique of Pure Reason, one of the most influential works in the history of the philosophy of space and time. He describes time as an a priori notion that, together with other a priori notions such as space, allows us to comprehend sense experience. Kant holds that neither space nor time are substance,
entities in themselves, or learned by experience; he holds, rather,
that both are elements of a systematic framework we use to structure our
experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantitatively compare the interval between (or duration of) events. Although space and time are held to be transcendentally ideal in this sense, they are also empirically real—that is, not mere illusions.
Some idealist writers, such as J. M. E. McTaggart in The Unreality of Time, have argued that time is an illusion (see also The flow of time, below).
The writers discussed here are for the most part realists in this regard; for instance, Gottfried Leibniz held that his monads existed, at least independently of the mind of the observer.
Absolutism and relationalism
Leibniz and Newton
The
great debate between defining notions of space and time as real objects
themselves (absolute), or mere orderings upon actual objects (relational), began between physicists Isaac Newton (via his spokesman, Samuel Clarke) and Gottfried Leibniz in the papers of the Leibniz–Clarke correspondence.
Arguing against the absolutist position, Leibniz offers a number of thought experiments
with the purpose of showing that there is contradiction in assuming the
existence of facts such as absolute location and velocity. These
arguments trade heavily on two principles central to his philosophy: the
principle of sufficient reason and the identity of indiscernibles.
The principle of sufficient reason holds that for every fact, there is a
reason that is sufficient to explain what and why it is the way it is
and not otherwise. The identity of indiscernibles states that if there
is no way of telling two entities apart, then they are one and the same
thing.
The example Leibniz uses involves two proposed universes situated
in absolute space. The only discernible difference between them is that
the latter is positioned five feet to the left of the first. The
example is only possible if such a thing as absolute space exists. Such a
situation, however, is not possible, according to Leibniz, for if it
were, a universe's position in absolute space would have no sufficient
reason, as it might very well have been anywhere else. Therefore, it
contradicts the principle of sufficient reason, and there could exist
two distinct universes that were in all ways indiscernible, thus
contradicting the identity of indiscernibles.
Standing out in Clarke's (and Newton's) response to Leibniz's arguments is the bucket argument:
Water in a bucket, hung from a rope and set to spin, will start with a
flat surface. As the water begins to spin in the bucket, the surface of
the water will become concave. If the bucket is stopped, the water will
continue to spin, and while the spin continues, the surface will remain
concave. The concave surface is apparently not the result of the
interaction of the bucket and the water, since the surface is flat when
the bucket first starts to spin, it becomes concave as the water starts
to spin, and it remains concave as the bucket stops.
In this response, Clarke argues for the necessity of the existence of absolute space to account for phenomena like rotation and acceleration that cannot be accounted for on a purely relationalist account.
Clarke argues that since the curvature of the water occurs in the
rotating bucket as well as in the stationary bucket containing spinning
water, it can only be explained by stating that the water is rotating in
relation to the presence of some third thing—absolute space.
Leibniz describes a space that exists only as a relation between
objects, and which has no existence apart from the existence of those
objects. Motion exists only as a relation between those objects.
Newtonian space provided the absolute frame of reference within which
objects can have motion. In Newton's system, the frame of reference
exists independently of the objects contained within it. These objects
can be described as moving in relation to space itself. For almost two
centuries, the evidence of a concave water surface held authority.
Mach
Another important figure in this debate is 19th-century physicist Ernst Mach.
While he did not deny the existence of phenomena like that seen in the
bucket argument, he still denied the absolutist conclusion by offering a
different answer as to what the bucket was rotating in relation to: the
fixed stars.
Mach suggested that thought experiments like the bucket argument
are problematic. If we were to imagine a universe that only contains a
bucket, on Newton's account, this bucket could be set to spin relative
to absolute space, and the water it contained would form the
characteristic concave surface. But in the absence of anything else in
the universe, it would be difficult to confirm that the bucket was
indeed spinning. It seems equally possible that the surface of the water
in the bucket would remain flat.
Mach argued that, in effect, the water experiment in an otherwise
empty universe would remain flat. But if another object were introduced
into this universe, perhaps a distant star, there would now be
something relative to which the bucket could be seen as rotating. The
water inside the bucket could possibly have a slight curve. To account
for the curve that we observe, an increase in the number of objects in
the universe also increases the curvature in the water. Mach argued that
the momentum of an object, whether angular or linear, exists as a
result of the sum of the effects of other objects in the universe (Mach's Principle).
Einstein
Albert Einstein proposed that the laws of physics should be based on the principle of relativity.
This principle holds that the rules of physics must be the same for all
observers, regardless of the frame of reference that is used, and that
light propagates at the same speed in all reference frames. This theory
was motivated by Maxwell's equations, which show that electromagnetic waves propagate in a vacuum at the speed of light.
However, Maxwell's equations give no indication of what this speed is
relative to. Prior to Einstein, it was thought that this speed was
relative to a fixed medium, called the luminiferous ether.
In contrast, the theory of special relativity postulates that light
propagates at the speed of light in all inertial frames, and examines
the implications of this postulate.
All attempts to measure any speed relative to this ether failed,
which can be seen as a confirmation of Einstein's postulate that light
propagates at the same speed in all reference frames. Special relativity
is a formalization of the principle of relativity that does not contain
a privileged inertial frame of reference, such as the luminiferous
ether or absolute space, from which Einstein inferred that no such frame
exists.
Einstein generalized relativity to frames of reference that were non-inertial. He achieved this by positing the Equivalence Principle,
which states that the force felt by an observer in a given
gravitational field and that felt by an observer in an accelerating
frame of reference are indistinguishable. This led to the conclusion
that the mass of an object warps the geometry of the space-time
surrounding it, as described in Einstein's field equations.
In classical physics, an inertial reference frame is one in which
an object that experiences no forces does not accelerate. In general
relativity, an inertial frame of reference is one that is following a geodesic of space-time. An object that moves against a geodesic experiences a force. An object in free fall
does not experience a force, because it is following a geodesic. An
object standing on the earth, however, will experience a force, as it is
being held against the geodesic by the surface of the planet.
Einstein partially advocates Mach's principle
in that distant stars explain inertia because they provide the
gravitational field against which acceleration and inertia occur. But
contrary to Leibniz's account, this warped space-time is as integral a
part of an object as are its other defining characteristics, such as
volume and mass. If one holds, contrary to idealist beliefs, that
objects exist independently of the mind, it seems that relativistics
commits them to also hold that space and temporality have exactly the
same type of independent existence.
Conventionalism
The
position of conventionalism states that there is no fact of the matter
as to the geometry of space and time, but that it is decided by
convention. The first proponent of such a view, Henri Poincaré, reacting to the creation of the new non-Euclidean geometry,
argued that which geometry applied to a space was decided by
convention, since different geometries will describe a set of objects
equally well, based on considerations from his sphere-world.
This view was developed and updated to include considerations from relativistic physics by Hans Reichenbach. Reichenbach's conventionalism, applying to space and time, focuses around the idea of coordinative definition.
Coordinative definition has two major features. The first has to
do with coordinating units of length with certain physical objects. This
is motivated by the fact that we can never directly apprehend length.
Instead we must choose some physical object, say the Standard Metre at
the Bureau International des Poids et Mesures (International Bureau of Weights and Measures), or the wavelength of cadmium
to stand in as our unit of length. The second feature deals with
separated objects. Although we can, presumably, directly test the
equality of length of two measuring rods when they are next to one
another, we can not find out as much for two rods distant from one
another. Even supposing that two rods, whenever brought near to one
another are seen to be equal in length, we are not justified in stating
that they are always equal in length. This impossibility undermines our
ability to decide the equality of length of two distant objects.
Sameness of length, to the contrary, must be set by definition.
Such a use of coordinative definition is in effect, on
Reichenbach's conventionalism, in the General Theory of Relativity where
light is assumed, i.e. not discovered, to mark out equal distances in
equal times. After this setting of coordinative definition, however, the
geometry of spacetime is set.
As in the absolutism/relationalism debate, contemporary
philosophy is still in disagreement as to the correctness of the
conventionalist doctrine.
Structure of space-time
Building from a mix of insights from the historical debates of
absolutism and conventionalism as well as reflecting on the import of
the technical apparatus of the General Theory of Relativity, details as
to the structure of space-time have made up a large proportion of discussion within the philosophy of space and time, as well as the philosophy of physics. The following is a short list of topics.
Relativity of simultaneity
According to special relativity each point in the universe can have a different set of events that compose its present instant. This has been used in the Rietdijk–Putnam argument to demonstrate that relativity predicts a block universe in which events are fixed in four dimensions.
Invariance vs. covariance
Bringing
to bear the lessons of the absolutism/relationalism debate with the
powerful mathematical tools invented in the 19th and 20th century, Michael Friedman draws a distinction between invariance upon mathematical transformation and covariance upon transformation.
Invariance, or symmetry, applies to objects, i.e. the symmetry group of a space-time theory designates what features of objects are invariant, or absolute, and which are dynamical, or variable.
Covariance applies to formulations of theories, i.e. the covariance group designates in which range of coordinate systems the laws of physics hold.
This distinction can be illustrated by revisiting Leibniz's
thought experiment, in which the universe is shifted over five feet. In
this example the position of an object is seen not to be a property of
that object, i.e. location is not invariant. Similarly, the covariance
group for classical mechanics
will be any coordinate systems that are obtained from one another by
shifts in position as well as other translations allowed by a Galilean transformation.
In the classical case, the invariance, or symmetry, group and the
covariance group coincide, but they part ways in relativistic physics.
The symmetry group of the general theory of relativity includes all
differentiable transformations, i.e., all properties of an object are
dynamical, in other words there are no absolute objects. The
formulations of the general theory of relativity, unlike those of
classical mechanics, do not share a standard, i.e., there is no single
formulation paired with transformations. As such the covariance group of
the general theory of relativity is just the covariance group of every
theory.
Historical frameworks
A
further application of the modern mathematical methods, in league with
the idea of invariance and covariance groups, is to try to interpret
historical views of space and time in modern, mathematical language.
In these translations, a theory of space and time is seen as a manifold paired with vector spaces,
the more vector spaces the more facts there are about objects in that
theory. The historical development of spacetime theories is generally
seen to start from a position where many facts about objects are
incorporated in that theory, and as history progresses, more and more
structure is removed.
For example, Aristotelian space and time has both absolute
position and special places, such as the center of the cosmos, and the
circumference. Newtonian space and time has absolute position and is Galilean invariant, but does not have special positions.
Holes
With the
general theory of relativity, the traditional debate between absolutism
and relationalism has been shifted to whether spacetime is a substance,
since the general theory of relativity largely rules out the existence
of, e.g., absolute positions. One powerful argument against spacetime substantivalism, offered by John Earman is known as the "hole argument".
This is a technical mathematical argument but can be paraphrased as follows:
Define a function d as the identity function over all elements over the manifold M, excepting a small neighbourhood H belonging to M. Over H d comes to differ from identity by a smooth function.
With use of this function d we can construct two mathematical models, where the second is generated by applying d to proper elements of the first, such that the two models are identical prior to the time t=0, where t is a time function created by a foliation of spacetime, but differ after t=0.
These considerations show that, since substantivalism allows the
construction of holes, that the universe must, on that view, be
indeterministic. Which, Earman argues, is a case against
substantivalism, as the case between determinism or indeterminism should
be a question of physics, not of our commitment to substantivalism.
Direction of time
The problem of the direction of time arises directly from two contradictory facts. Firstly, the fundamental physical laws are time-reversal invariant;
if a cinematographic film were taken of any process describable by
means of the aforementioned laws and then played backwards, it would
still portray a physically possible process. Secondly, our experience of
time, at the macroscopic level, is not time-reversal invariant.
Glasses can fall and break, but shards of glass cannot reassemble and
fly up onto tables. We have memories of the past, and none of the
future. We feel we can't change the past but can influence the future.
Causation solution
One solution to this problem takes a metaphysical view, in which the direction of time follows from an asymmetry of causation.
We know more about the past because the elements of the past are causes
for the effect that is our perception. We feel we can't affect the past
and can affect the future because we can't affect the past and can affect the future.
There are two main objections to this view. First is the problem
of distinguishing the cause from the effect in a non-arbitrary way. The
use of causation in constructing a temporal ordering could easily become
circular. The second problem with this view is its explanatory power.
While the causation account, if successful, may account for some
time-asymmetric phenomena like perception and action, it does not
account for many others.
However, asymmetry of causation can be observed in a
non-arbitrary way which is not metaphysical in the case of a human hand
dropping a cup of water which smashes into fragments on a hard floor,
spilling the liquid. In this order, the causes of the resultant pattern
of cup fragments and water spill is easily attributable in terms of the
trajectory of the cup, irregularities in its structure, angle of its
impact on the floor, etc. However, applying the same event in reverse,
it is difficult to explain why the various pieces of the cup should fly
up into the human hand and reassemble precisely into the shape of a cup,
or why the water should position itself entirely within the cup. The
causes of the resultant structure and shape of the cup and the
encapsulation of the water by the hand within the cup are not easily
attributable, as neither hand nor floor can achieve such formations of
the cup or water. This asymmetry is perceivable on account of two
features: i) the relationship between the agent capacities of the human
hand (i.e., what it is and is not capable of and what it is for) and
non-animal agency (i.e., what floors are and are not capable of and what
they are for) and ii) that the pieces of cup came to possess exactly
the nature and number of those of a cup before assembling. In short,
such asymmetry is attributable to the relationship between i) temporal
direction and ii) the implications of form and functional capacity.
The application of these ideas of form and functional capacity
only dictates temporal direction in relation to complex scenarios
involving specific, non-metaphysical agency which is not merely
dependent on human perception of time. However, this last observation in
itself is not sufficient to invalidate the implications of the example
for the progressive nature of time in general.
Thermodynamics solution
The
second major family of solutions to this problem, and by far the one
that has generated the most literature, finds the existence of the
direction of time as relating to the nature of thermodynamics.
The answer from classical thermodynamics states that while our basic physical theory is, in fact, time-reversal symmetric, thermodynamics is not. In particular, the second law of thermodynamics states that the net entropy of a closed system never decreases, and this explains why we often see glass breaking, but not coming back together.
But in statistical mechanics
things become more complicated. On one hand, statistical mechanics is
far superior to classical thermodynamics, in that thermodynamic
behavior, such as glass breaking, can be explained by the fundamental
laws of physics paired with a statistical
postulate. But statistical mechanics, unlike classical thermodynamics,
is time-reversal symmetric. The second law of thermodynamics, as it
arises in statistical mechanics, merely states that it is overwhelmingly likely that net entropy will increase, but it is not an absolute law.
Current thermodynamic solutions to the problem of the direction
of time aim to find some further fact, or feature of the laws of nature
to account for this discrepancy.
Laws solution
A
third type of solution to the problem of the direction of time,
although much less represented, argues that the laws are not
time-reversal symmetric. For example, certain processes in quantum mechanics, relating to the weak nuclear force,
are not time-reversible, keeping in mind that when dealing with quantum
mechanics time-reversibility comprises a more complex definition. But
this type of solution is insufficient because 1) the time-asymmetric
phenomena in quantum mechanics are too few to account for the uniformity
of macroscopic time-asymmetry and 2) it relies on the assumption that
quantum mechanics is the final or correct description of physical
processes.
One recent proponent of the laws solution is Tim Maudlin
who argues that the fundamental laws of physics are laws of temporal
evolution (see Maudlin [2007]). However, elsewhere Maudlin argues:
"[the] passage of time is an intrinsic asymmetry in the temporal
structure of the world... It is the asymmetry that grounds the
distinction between sequences that runs from past to future and
sequences which run from future to past" [ibid, 2010 edition, p. 108].
Thus it is arguably difficult to assess whether Maudlin is suggesting
that the direction of time is a consequence of the laws or is itself
primitive.
Flow of time
The problem of the flow of time, as it has been treated in analytic philosophy, owes its beginning to a paper written by J. M. E. McTaggart,
in which he proposes two "temporal series". The first series, which
means to account for our intuitions about temporal becoming, or the
moving Now, is called the A-series. The A-series orders events according to their being in the past, present or future, simpliciter and in comparison to each other. The B-series
eliminates all reference to the present, and the associated temporal
modalities of past and future, and orders all events by the temporal
relations earlier than and later than.
McTaggart, in his paper "The Unreality of Time",
argues that time is unreal since a) the A-series is inconsistent and b)
the B-series alone cannot account for the nature of time as the
A-series describes an essential feature of it.
Building from this framework, two camps of solution have been
offered. The first, the A-theorist solution, takes becoming as the
central feature of time, and tries to construct the B-series from the
A-series by offering an account of how B-facts come to be out of
A-facts. The second camp, the B-theorist solution, takes as decisive
McTaggart's arguments against the A-series and tries to construct the
A-series out of the B-series, for example, by temporal indexicals.
Dualities
Quantum field theory models have shown that it is possible for theories in two different space-time backgrounds, like AdS/CFT or T-duality, to be equivalent.
Presentism and eternalism
According to Presentism, time is an ordering of various realities.
At a certain time some things exist and others do not. This is the only
reality we can deal with and we cannot for example say that Homer exists because at the present time he does not. An Eternalist,
on the other hand, holds that time is a dimension of reality on a par
with the three spatial dimensions, and hence that all things—past,
present and future—can be said to be just as real as things in the
present. According to this theory, then, Homer really does exist,
though we must still use special language when talking about somebody
who exists at a distant time—just as we would use special language when
talking about something far away (the very words near, far, above, below, and such are directly comparable to phrases such as in the past, a minute ago, and so on).
Endurantism and perdurantism
The positions on the persistence of objects are somewhat similar. An endurantist
holds that for an object to persist through time is for it to exist
completely at different times (each instance of existence we can regard
as somehow separate from previous and future instances, though still
numerically identical with them). A perdurantist
on the other hand holds that for a thing to exist through time is for
it to exist as a continuous reality, and that when we consider the thing
as a whole we must consider an aggregate of all its "temporal parts"
or instances of existing. Endurantism is seen as the conventional view
and flows out of our pre-philosophical ideas (when I talk to somebody I
think I am talking to that person as a complete object, and not just a
part of a cross-temporal being), but perdurantists such as David Lewis
have attacked this position. They argue that perdurantism is the
superior view for its ability to take account of change in objects.
On the whole, Presentists are also endurantists and Eternalists
are also perdurantists (and vice versa), but this is not a necessary
relation and it is possible to claim, for instance, that time's passage
indicates a series of ordered realities, but that objects within these
realities somehow exist outside of the reality as a whole, even though
the realities as wholes are not related. However, such positions are
rarely adopted.
