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Space of itself, and time of itself will sink into mere shadows, and only a kind of union between them shall survive.


Hermann Minkowski

[in Feynman R., Lieghton R., and Sands M., The Feynman Lectures on Physics Vol. I,

(Addison-Wesley, Reading, MA, 1963) p. 17-8.]

Is Space-Time Galilean or Minkowski?

Classical physics views space-time as consisting of three orthogonal spatial dimensions (Euclidean space) in which all physical processes evolve according to an absolute time. When matter was thought to consist of solid particles (made of something like sticky billiard balls) this implied that moving clocks would tick at the same rate as stationary clocks. However, a classical wave theory of matter requires that moving clocks tick more slowly than stationary clocks. The simple explanation for this is that circular (or oscillating) wave orbits of matter in a stationary clock become longer helical (or cycloidal or sinusoidal) orbits in a moving clock. If each wave orbit constitutes a tick of the clock then the moving clock ticks more slowly. This phenomenon is referred to as relativistic 'time dilation'.

This explanation of relativistic time dilation may lead you to believe that it is possible to compare clocks and determine absolute motion relative to the underlying medium (i.e. the aether). That is not the case because signals passed back and forth between clocks with relative motion will be Doppler shifted. The form of the Doppler shift depends on whether the source or the detector of the signal is moving. Hence without a priori knowledge of which clock is actually moving it is impossible to know how the signal is Doppler shifted. If an observer simply assumes that their clock is stationary then any error in the resulting estimate of the Doppler shift will exactly cancel the error in estimating the relative ticking rates of the clocks. The clock which appears to be moving will also appear to tick slowly.

If matter consists of waves then the distance between two points is  proportional to the wave propagation time between those points. Since a moving clock ticks slowly compared to a stationary clock, an object appears to be shorter (by the same reduction factor as the clock speed) when moving than when stationary.  This phenomenon is called relativistic 'length contraction'.

According to the theory of Special Relativity, distance and time measurements in differently moving reference frames are related by Lorentz transformations which embody length contraction and time dilation. A space whose distance and time measurements transform via Lorentz transformations is called 'Minkowski space' (or Einstein-Minkowski space). All physical measurements, forming our 'measurement space'  are consistent with this Minkowski space. However, given that matter consists of waves, the physical space in which those waves propagate must be Galilean in order to yield a measurement space which is Minkowski.

For more detail go to Chapter 2 of The Classical Theory of Matter Waves


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

Copyright 2006-2007  Robert A. Close