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The first precept was never to accept a thing as true until I knew it as such without a single doubt.

René DesCartes

Discours de la Méthode (1637)

Is Space Curved?

    Classical physics views space as consisting of three orthogonal spatial dimensions (Euclidean or 'flat' space). This belief was challenged by Einstein's theory of General Relativity which predicts space to be curved (non-Euclidean). For example, the measured  difference in circumference of two circles around the earth would not be exactly proportional to the difference of the measured radii. This discrepancy from Euclidean geometry has measurable consequences (affecting the GPS navigational system, for example). The ‘curved space’ which is associated with general relativity can be interpreted classically by supposing the speed of light and matter waves to decrease slightly in the vicinity of matter (a prediction of General Relativity). This interpretation of gravity results in mutual attraction because waves always refract toward regions of decreased wave speed. In a solid aether, the reduced wave speed can be attributed to a compression of the solid  in the vicinity of matter waves. The reduced speed of light near a massive object such as the earth causes the wavelength to decrease toward the center of the object, so that a circumference measurement would yield a propagation time (or number of wavelengths) less than p times the propagation time across the diameter. Hence the measured geometry appears to be non-Euclidean even if absolute space is 'flat'.

For more detail go to Chapter 4 of The Classical Theory of Matter Waves.


Created: 27 February 2006;  Last updated: 08 January 2007

Copyright © 2006-2007  Robert A. Close