Philosophy of space and time

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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, focusses the subject into a number of basic issues.

Contents

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 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. 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 its 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 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 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, 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 (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

With the GTR, the traditional debate between absolutism and relationalism has been shifted to the question as 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 a more metaphysical tack. 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 views consistency, 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 get 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, 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 by 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 assymmetry 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 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.

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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