last revised November 29th, 2004.See Lowe chapter 14.
So far we have been looking almost entirely at things, events, etc. We have sometimes noted that spatio-temporal matters impinge on our understanding of these things (a lot of the mystery of views of substances and universals involve space-time; the identity of indiscernibles may be a lot more acceptable if spatio-temporal properties are excluded; etc.) but we haven't said much about space and time themselves (or space-time itself).
Discussion of these issues displays the picture common to metaphysics of disparate kinds of consideration being invoked to support one position rather than another. There are appeals to verificationism or principles of sufficient reason (often by relationalists such as Leibniz arguing against absolute notions of space-time); there are appeals to scientific theory or even observational evidence (as by Newton in defence of absolutism); there are appeals to possibilities (is there a difference between a universe consisting of just one disk at rest and another with the same disk rotating?). In what follows, I shall stick pretty closely to what Lowe offers in his survey of the issues.
Lowe starts with the claim that we think of space as three-dimenionsal; is it proper to take time as a fourth dimension of something we call space-time? He says we don't think of time as anything like space, but physics treats it as a fourth dimension. (Check Schwartz' text [chapter 8 of his on-line book, Beyond Experience: Metaphysical Theories and Philosophical Constraints] for some material taken from Taylor on how we might begin to think of time as much more like space than Lowe supposes.)
For space, there is a contrast between a bottom-up view (space composed of points) and a top-down view (global space is fundamental; can't compose something out of zero-dimensional points, even an uncountable infinity of them). He will come back to this in Chapter 16. But he wants to say that space is not composed of its 3-dimensional parts; space as a whole is unitary. Seems to have some global properties (finite or infinite; curvature [0 according to Euclid, variable in Einstein's General Relativity]; topology [there is a famous argument about handedness, due originally to Kant, that seems to support the idea of topological properties belonging to a space as a whole]).
But what is this space? Some have thought of a void, but that seems just like nothing at all. Others have regarded it as a plenum, full of something or other - matter for Descartes; energy for some of us. (The QM vacuum is energetic.) But General Relativity seems to permit completely empty spacetimes, so we seem to get close to Newton's absolute space: an infinite, unitary, immaterial substance (which is itself uncomfortably close to traditional views of God).
Newton's position is that we are mostly only able to discover relative motions, but that we can invoke an absolute space and thus unknowable absolute motions because we do have access to evidence for absolute accelerations. Newton assumed that if there is absolute acceleration then there must be absolute velocity and absolute location. [I think it is now agreed that this inference is invalid. We can have mathematical theories of physics that licence absolute accelerations but without postulating the geometric structure that is needed for absolute velocity or location.]
Lowe mentions two thought experiments Newton offered as demonstrating absolute accelerations: the rotating bucket and the two globes. The bucket phenomenon is actually observable. Start with a bucket of water, hanging on a rope. Water and bucket are stationary; no relative motion between water and bucket. Twirl the bucket on its rope and then let spin back. The bucket spins rapidly; there is relative motion between water and bucket. Near the end of this stage the water picks up the motion of the bucket and so there is now no longer any relative motion between water and bucket (as at the beginning). But unlike at the beginning, the water is now concave, while at the start it was flat. Newton's explanation: at the start it wasn't accelerating; at the end it is rotating (which is a form of acceleration), but not relative to the bucket, so relative to [absolute] space.
Mach's famous objection is: OK it's not rotating relative to the bucket but to the rest of the material universe. The two globes example is a real thought experiment which Lowe sees as a partial response to this line of argument. Suppose the universe is simply two globes tied together on a string. Newton supposes that there is a distinguishable difference between two such globes at rest and the two globes rotating around the centre of the string - because in the latter case there would be a tension on the string (cf. whirling a stone on a string round your head). There is no difference of relative motion in the two cases. But now Mach's objection is why assume that's how it would be? If there is nothing but the two globes, maybe there would be no tension in the string.
Lowe's conclusion: both sides invoke mysteries. Newton has acceleration relative to Space causing effects, but Mach has apparently instantaneous creation of mass by existence of other bodies. Newton (and common sense) takes mass to be an intrinsic property of a body; for Mach it is a relation.
Lowe goes on to consider varieties of relationalist view. One extreme position is that space as such does not exist, only spatial relations between bodies. But then what is a place actually unoccupied by any body? (This is the problem of the vacuum for relationalists. Lowe distinguishes (a) completely empty space, which you might think is impossible, from (b) an empty portion of space, which seems conceivable.) A less extreme view: space does exist but it depends on material bodies which occupy it, and their spatial relations. But then how could we tell whether space is bounded? Lowe takes a sample universe with three material particles in a triangular arrangement. It appears that the properties of space depend on those particles, but how could we determine whether space is infinite in this universe?
By way of an answer, a relationalist might say space depends on what it is possible for objects to do, so the laws of nature of the universe dictate the nature of space. Lowe thinks this the only relationalist view that might work. Not clear it is bettter than Newton's. Lowe points out that Einstein's General Theory of Relativity can be construed as simply updating Newtonian space. It replaces Newton's idea of matter and mass, but what it suggests instead is that mass is a deformation of the curvature of spacetime.
Lowe ends with a brief remark about Special Relativity and time. Einstein certainly differs from Newton in that Newton thought time a separate entity from space; he operated with a notion of absolute simultaneity whereas for Einstein time determinations are all relative to a frame of reference. Einstein postulates the constancy of the velocity of light in all frames of reference and this entails that events that are judged simultaneous in one frame of reference may not be simultaneous in another. What is absolute for Einstein is the space-time separation of events.
Lowe remarks that what we can measure empirically is the average two-way velocity of light from A to B and back again. Our access to that does not establish that light took the same time to go from A to B as from B to A. Einstein, influenced probably by Mach and other positivist thinkers, actually said here that we must simply define the one-way velocity.
Lowe's conclusion is that we don't have to assume that Einstein has the last word.
© Ed Brandon, 2004.
last revised November 29th, 2004.
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