Philosophy of time

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.

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 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, 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.