Philosophy of space and 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, focusses the subject into a number of basic issues.
- Absolutism vs. Relationalism
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.
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 sufficent 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. 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. Since, Clarke argues, the curvature of the water in the rotating bucket can only be explained by stating that the bucket is rotating, and that the relational facts about the bucket are the same for the stationary and rotating bucket, then the bucket must be rotating in relation to some third thing, namely absolute space.
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 argues that thought experiments like the bucket argument are problematic because we cannot reason as to what would happen in a universe with only a bucket and otherwise empty. A bucket rotating on the earth is different relationally from one at rest, e.g. in it's relation to the tree from which the rope is hanging. While the surrounding matter of the tree, the earth and the universe in general would seem inconsequential, Mach argues to the contrary pioneering Mach's principle.
Perhaps the most famous relationalist is Albert Einstein who saw his General Theory of Relativity as vindicating Mach's intuition that the fixed stars play a part in which motions are inertial and which aren't, by offering a rigorous scientific formulization.
Contemporary philosophy, however, is not quite as unanimous about the import of the GTR on the absolutism/relationalism debate. One popular line of thinking believes that the results are mixed. While the GTR offers the relationalist success, by placing views in which there are absolute facts about position, velocity and acceleration in a compromised position, so too is classic relationalism compromised by the existence of solutions to the equations of the GTR in which the universe is empty of matter.
- 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 Meter at the International Bureau of Weights and Measures, or the wavelength of cadmium to stand in as our unit of length. The second feature deals with seperated 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 GTR 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, a distinction was drawn 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 (mathematics) 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
Space Invaders
- The direction of time
- The flow of time