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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 ie 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 andb) 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 eg 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 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


    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 ie 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 ie the symmetry group of a spacetime theory designates what features of objects are invariant or absolute and which are dynamical or variable
    Covariance applies to formulations of theories ie 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 ie 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 ie 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 ie 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


    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, eg 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

    The direction of time

    The problem of the direction of time arises directly from two contradictory facts Firstly the laws of nature ie 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 ie 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


    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


    • 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 DH (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