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Philosophy of space and time is a branch
of philosophy which deals with issues surrounding the ontology,
epistemology and character of space and time. While this type
of study has been central to philosophy from its inception,
the philosophy of space and time, an inspiration for, and
central to early analytic philosophy, focuses the subject
into a number of basic issues.
Realism and anti-realism
A traditional realist position in ontology
is that time and space have existence apart from the human
mind. Idealists 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.
Kant, in the Critique of Pure Reason, described
time as an a priori notion that, together with other a priori
notions such as space, allows us to comprehend sense experience.
For Kant, neither space nor time are conceived as substances,
but rather 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.
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 vs. relationalism
Leibniz and Newton
The debate between whether space and time
are real objects themselves, i.e absolute, or merely orderings
upon real objects, i.e. relational, began with a debate between
Isaac Newton, through his spokesman Samuel Clarke, and Gottfried
Leibniz in the famous Leibniz-Clarke Correspondence.
Arguing against the absolutist position, Leibniz
offers a number of thought experiments aiming to show that
assuming the existence of facts such as absolute location
and velocity will lead to contradiction. These arguments trade
heavily on two principles central to Leibniz's 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 sufficient to explain 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.
For example, Leibniz asks us to imagine two
universes situated in absolute space. The only difference
between them is that the second is placed five feet to the
left of the first, a possibility available if such a thing
as absolute space exists. Such a situation, however, is not
possible according to Leibniz, for if it were:
a) where a universe was positioned in absolute
space would have no sufficient reason, as it might very well
have been anywhere else, hence contradicting the principle
of sufficient reason, and
b) there could exist two distinct universes that were in all
ways indiscernible, hence contradicting the Identity of Indiscernibles.
Standing out in Clarke's, and Newton's, response to Leibniz
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 water is flat when the bucket first starts to spin,
becomes concave as the water starts to spin, and 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 some third thing, namely absolute space.
Leibniz describes a space that exists only
as a relation between objects, and which therefore has no
existence apart from the existence of those objects; motion
exists only as a relation between those objects. Newtonian
space provided an absolute frame of reference within which
objects can have motion. In Newton's system the frame of reference
exists independently of the objects which it contains; objects
can be described as moving in relation to space itself. For
two hundred years, the empirical evidence of the concave water
surface held sway.
Mach
Stepping into this debate in the 19th century
is Ernst Mach. Not denying 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 suggests that thought experiments like
the bucket argument are problematic. Imagine a universe containing
only 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, how could one confirm
that the bucket was indeed spinning? It seems at least equally
possible that the surface of the water in the bucket would
remain flat.
Mach argued, in effect, that the water in
a bucket in an otherwise empty universe would indeed remain
flat. But introduce another object into the universe - a distant
star, perhaps - and there is now something relative to which
the bucket could be seen to be rotating. The water might now
adopt a slight curve. As the number of objects in the universe
increased, so the curvature of the water, up to the point
that we see in the actual universe. In effect Mach argued
that the momentum of an object, angular or linear, exists
as a result of the sum of the effects of other objects in
the universe - Mach's principle.
Einstein
Einstein's relativistics are based on the principle
of relativity, which holds that the rules of physics must be
the same for all observers, regardless of the frame of reference
they use. The greatest difficulty for this idea were Maxwell's
equations which included the speed of light in vacuum, implying
that the speed of light is only constant relative to the postulated
luminiferous ether. However, all attempts to measure any speed
relative to the ether failed. Einstein showed how special relativity's
Lorentz transformations can be derived from the principle of
relativity and the invariance of light speed. Special relativity
is a formalisation of the principle of relativity which does
not contain a privileged inertial frame of reference such as
the luminiferous aether or absolute space, from which Einstein
inferred that no such frame exists. That philosophical approach
has become popular among physicists. These views of space and
time were also strongly influenced by mathematicians such as
Minkowski, according to whom only a kind of union of [space
and time] will preserve an independent reality.
Einstein generalised relativity to frames
of reference that were non-inertial. He achieved this by positing
the Equivalence Principle, that the force felt by an observer
in a gravitational field and that felt by an observer in an
accelerating frame of reference were indistinguishable. This
led to the remarkable conclusion that the mass of an object
warps the geometry of the space surrounding it, as described
in Einstein's field equations.
An inertial frame of reference is one that
is following a geodesic of spacetime. An object that moves
against a geodesic experiences a force. For example, an object
in free fall does not experience a force, because it is following
a geodesic. An object standing on the earth will experience
a force, as it is being held against the geodesic by the surface
of the planet.
A bucket of water rotating in empty space
will experience a force because it rotates with respect to
the geodesic. The water will become concave, not because it
is rotating with respect to the distant stars, but because
it is rotating with respect to the geodesic.
Einstein partially vindicates Mach's principle,
in that the distant stars explain inertia in so far as they
provide the gravitational field against which acceleration,
and inertia, occur. But contrary to Leibniz' account, this
warped spacetime is as much a part of an object as are its
mass and volume. If one holds, contrary to the idealists,
that there are objects that exist independently of the mind,
it seems that Relativistics commits one to also hold that
space and time have the same sort 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 Poincare, 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,
focusses 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. While conventionalism
still holds many proponents, cutting criticisms concerning
the coherence of Reichenbach's doctrine of coordinative definition
have led many to see the conventionalist view as untenable.
The structure of spacetime
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 spacetime 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.
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, interestingly
enough, they part ways in relativistic physics. The symmetry
group of the GTR 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 GTR,
unlike that 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 GTR 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 or incorporated in that theory, and as history
progresses, more and more structure is removed.
For example, Aristotle's theory of space and
time holds that not only is there such a thing as absolute
position, but that there are special places in space, such
as a center to the universe, a sphere of fire, etc. Newtonian
spacetime has absolute position, but not special positions.
Galilean spacetime has absolute acceleration, but not absolute
position or velocity. And so on.
Holes
With the GTR, the traditional debate between
absolutism and relationalism has been shifted to whether or
not spacetime is a substance, since the GTR 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
(topology) 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.
The direction of time
The problem of the direction of time arises directly
from two contradictory facts. Firstly, the laws of nature, i.e.
our fundamental physics, are time-reversal invariant. In other
words, the laws of physics are such that anything that can happen
moving forward through time is just as possible moving backwards
in time. Or, put in another way, through the eyes of physics,
there will be no distinction, in terms of possibility, between
what happens in a movie if the film is run forward, or if the
film is run backwards. The second fact is that our experience
of time, at the macroscopic level, is not time-reversal invariant.
Glasses fall and break all the time, but shards of glass do
not put themselves back together and fly up on tables. We have
memories of the past, and none of the future. We feel we can't
change the past but can affect the future.
The causation solution
One of the two major families of solution to
this problem takes more of a metaphysical view. In this view
the existence of a direction of time can be traced to 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.
And so on.
Traditionally, there are seen to be two major
difficulties with this view. The most important is the difficulty
of defining causation in such a way that the temporal priority
of the cause over the effect is not so merely by stipulation.
If that is the case, our use of causation in constructing
a temporal ordering will be circular. The second difficulty
doesn't challenge the consistency of this view, but its explanatory
power. While the causation account, if successful may account
for some temporally asymmetric phenomena like perception and
action, it does not account for many other time asymmetric
phenomena, like the breaking glass described above.
The thermodynamics solution
The second major family of solution 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.
While this would seem a satisfactory answer,
unfortunately it was not meant to last. With the invention
of statistical mechanics things got more complicated. On one
hand, statistical mechanics is far superior to classical thermodynamics,
in that it can be shown that thermodynamic behavior, glass
breaking, can be explained by the fundamental laws of physics
paired with a statistical postulate. On the other hand, however,
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.
The 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 deemed as not time-reversible, keeping
in mind that when dealing with quantum mechanics time-reversibility
is comprised of a more complex definition.
Most commentators find this type of solution
insufficient because a) the types of phenomena in QM that
are time-reversal symmetric are too few to account for the
uniformity of time-reversal asymmetry at the macroscopic level
and b) there is no guarantee that QM is the final or correct
description of physical processes.
One recent proponent of the laws solution
is Tim Maudlin who argues that, in addition to quantum mechanical
phenomena, our basic spacetime physics, i.e. the General Theory
of Relativity, is time-reversal asymmetric. This argument
is based upon a denial of the types of definitions, often
quite complicated, that allow us to find time-reversal symmetries,
arguing that these definitions themselves are the cause of
there appearing to be a problem of the direction of time.
The 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 this paper McTaggart introduces
two temporal series that are central to our understanding of
time. 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, which does not worry at all about the "when"
of the present moment, orders all events as 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 spacetime backgrounds,
like AdS/CFT or T-duality, to be equivalent.
Quantum gravity
Quantum gravity calls into question many previously
held assumptions about spacetime.
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 are.
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 a long way away (the very words
near, far, above, below, over there 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 instances of
existing. Endurantism is seen as the conventional view and flows
out of our innate 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 perduranists have attacked
this position. (An example of a perdurantist is David Lewis.)
One argument perdurantists use to state the superiority of their
view is that perdurantism is able to take account of change
in objects.
The relations between these two questions
mean that on the whole presentists are also endurantists and
eternalists are perdurantists and vice versa, but this is
not necessary 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 hard to defend
and rarely adopted.
References
Albert, David (2000) Time and Chance.
Harvard
Earman, John (1989). World Enough and Space-Time. MIT
Friedman, Michael (1983) Foundations of Space-Time
Theories. Princeton
Grunbaum, Adolf (1974) Philosophical Problems of Space
and Time, 2nd Ed. Boston Studies in the Philosophy of Science.
Vol XII. D. Reidel Publishing
Horwich, Paul (1987) Asymmetries in Time. MIT Press
Mellor, D.H. (1998) Real Time II. Routledge
Reichenbach, Hans (1958) The Philosophy of Space and
Time. Dover
---(1991) The Direction of Time. University of California
Sklar, Lawrence (1976) Space, Time, and Spacetime.
University of California
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