Book review on absolute vs. relational theories of space and time

World Enough and Space-Time:  absolute versus relational theories of space and time
by John Earman (1989)


I loved this book.  For one thing, it’s the first philosophy book I’ve read that announces before the introduction that it will be using the Einstein summation convention.  The debate between Newton and Leibniz lives on among philosophers.  Do objects have spatial relations between them directly or by virtue of being embedded in space?  Is spacetime a substance or an abstraction?  Is there an absolute measure of motion, whether of velocity, acceleration, or rotation?  Professor Earman is refreshingly unafraid to extract ontological claims from physical theories and unimpressed by positivist reduction of the sciences.  In this, he is like the “new philosophers” who invented physics.  It was a pleasure, for instance, to read about Newton entertaining the proper Aristotelian question of whether space is to be regarded as a substance or an accident.  (He concludes it is neither, but a sort of necessary emanation of God.)

All of the famous arguments of the relationist vs. substantivalist debate are reviewed.  Leibniz and Huygens pointed to the Galilean invariance of the laws of nature to argue that all motion is relative.  Newton countered with his “bucket” argument:  one certainly can tell from centrifugal forces whether the water in a bucket is spinning, even though no relations between parts are changing.  Mach suggested that the distant fixed stars somehow pick out what is the inertial frame.  Leibniz thought that the reality of spacetime points would create an intolerable dilemma for God.  If everything in the universe were shifted a meter to the left, nothing would be different, so how could God decide which arrangement to make?  The strength of this argument will depend on how much weight one puts on Leibniz’ principle of sufficient reason.  Kant objected to the relationist thesis that it cannot account for the difference between a left and a right hand–all the internal relations are the same.

Earman clarifies the historical debate a great deal by translating it into the language of differential geometry.  For each spacetime ontology, certain things (distances, proper times, absolute acceleration, absolute movement) are and are not meaningful and unique, so different structures will be present on the spacetime manifold for use when one wants to write dynamical equations in covariant form.  For example, it’s amusing that the relationist’s position is worse in a genuinely 4D theory like relativity where there is a spacetime metric (not just a spatial or time metric) that picks out a unique spacetime connection, thus a unique definition of parallel transport and a unique measure of acceleration.  One actually has more freedom to build relational-friendly theories in a Newtonian-like spacetime.  (Newtonian physics requires the connection to be given.)

In Earman’s telling, the substantivalist’s case is consistently stronger than the relationists, until the last chapter where he somewhat reverses himself.  Earman uses Einstein’s “hole argument” to recast Leibniz’ argument against spacetime points in a form that doesn’t depend on a very questionable model of divine decision making.  Einstein was concerned that his field equations would not make unique predictions for the evolution of the metric.  The issue is not that matter distribution is insufficient to predict the spacetime.  (Spacetime has its own degrees of freedom corresponding to gravitational waves.)  That’s not a problem for determinism.  The problem is that the field equations are generally covariant, and a diffeomorphism of a solution is also a solution.  One could have two solutions related by a diffeomorphism that is the identity before a given time but different afterwards, and the theory cannot distinguish and predict one solution rather than the other.  Earman’s argument is not that this is wrong because philosophy somehow knows determinism to be true, but that philosophy should not be able to say a priori that determinism is false.  Hearing this argument, one is tempted to respond “So what?”  These “two solutions” are just the same physical solution in two different coordinate systems.  But Earman asks us to think in terms of active rather than passive diffeomorphisms:  moving events around to different spacetime points rather than changing coordinates.  My mind rebels against this:  how, absent some absolute background which general relativity doesn’t have, can one distinguish what one has done from a coordinate transformation?  But I think that’s Earman’s point.  If spacetime points had their own distinct existence independent of events on them, then we could label them (“A”, “B”, …) and it would be meaningful to say that our diffeomorphism had actually changed the system.  That most of us just assume that solutions related by diffeomorphism (members of a “Leibniz equivalence class” as Earman calls them) are physically the same shows an underlying relationism, an anti-realism with respect to spacetime points, in our thinking, although we probably are still substantivalists about spacetime in some deeper sense.

3 Responses

  1. I was just part of a great discussion of “World Enough and Space-Time: absolute versus relational theories of space and time by John Earman” on Facebook, said no one, ever.

  2. I ordered the book.

  3. great

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