mburns's Journal: Time for a Rewrite, Red and Blue Shifts are not so Simple.

The red and blue disks that I use to visualize changes from flat spacetime have opposite effects on space or time.

The red disks that represent the loss of a unit of time when crossed in the timelike direction make for a gain of a unit of length when crossed in the spacelike direction. Blue disks make for a gain in units of time and a loss of units of length when crossed. Remember that the centers for these red and blue disks are repeated or conserved in the relativistic direction of the orientation of the disks due to the Bianchi identities that apply to spacetime.

This opposite effect is so because of the opposite sign for timelike and spacelike directions in the metric. Extra dilation, red disks, that are purely timelike in one coordinate system can be crossed only spacially in another, that is for a well chosen interval. The timelike dilation, a loss of units of time, make the interval longer according to the rules of the metric. The other coordinate system can not disagree about the increased interval. So the same additional red disks crossed in the spacelike direction must represent a contraction of the spacial units, more of them are included.

Actually this correction simplifies the gravitational effects of these disks. Namely, red disks cause convergent curvature at their edges, and blue disks cause divergence. Remember that the rotation required by the loss or gain of units is hyperbolic for time and circular for space.

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Michael J. Burns