Thinking Straight About Curved Space | Issue 108 | Philosophy Now - 0 views
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In earlier columns, I have defended time from the assaults of physics. With a few exceptions, physicists have not been kind to time. Relativity theory stripped it of its tenses, dismissing the difference between past, present, and future as illusory. Worse, the theory seemed to deny time an independent existence.
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My own view, however, is that both space and time are traduced in physics. They should form a victim support group, which is why this column is devoted to a defence of space.
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Places – habitats – are stripped down to decimal places. Much is lost in consequence. The space of the physicist has neither ‘here’ nor ‘there’, no centre or periphery, no inside or outside, except in terms of relationships between points defined mathematically with respect to a frame of reference built out of axes whose (0,0,0) point of origin is arbitrarily chosen. The inhabitants of the physicists’ space are fields and objects that have only primary qualities – size, distance, number of instances. They are void of secondary qualities – warmth, brightness, colour, texture – never mind meaning, value, and use – even though all these qualities are inseparable from the space in which we experience, enact, and suffer our lives.
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So long as we don’t think that the physicists’ space is more fundamental than, or is the ultimate reality of, lived space, then no harm is done.
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in contemporary physics, space is curved, or non-Euclidean. In non-Euclidean space, the sum of the angles of a triangle may be greater than 180°; more importantly, the shortest distance between two points may not be a straight line, but a curved one.
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When we first hear talk of ‘curved space’ we rebel. The least we should ask of something said to be curved is that it should have edges, surfaces, and parts that look or feel curved, which space itself does not. Analogies are offered to make the idea less counter-intuitive
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Physicists will smile at taking the analogy too literally. But if it is not taken literally, it lacks explanatory force. And taken literally, it is seriously misleading. The curvature of an object such as the earth is extrinsic – evident in its surface
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From Pythagoras onwards we have been prone to the illusion that our ways of geometrising space capture space itself – perhaps even believing that the mathematical logic of pure quantities is somehow ‘out there’. However, the immense power of mathematical physics – which requires abstracting from phenomenal reality and the reduction of experienced and experienceable reality to mere parameters to which numerical values are assigned – does not justify uncritically accepting concepts such as ‘curved space’ that attempt to re-insert phenomenal appearances into its abstractions. On the contrary, we should acknowledge that ‘unreasonably effective’ mathematics (to borrow Eugene Wigner’s phrase) can take us to places to which nothing non-mathematical corresponds. For instance, consider the assumption, central to modern cosmology, that space itself is expanding.