Is the constancy of the speed of light dictated by special relativity invalidated by the expansion of the universe?

Yes it is. Special relativity is a 'local' theory of space-time that demands that space-time is flat ( Minkowskian) and that space does not change or dilate. General relativity which includes special relativity as a 'special case' is a global theory of space-time in which space can be curved due to gravitational fields. It is general relativity that predicts the expansion of space as a possible solution to the geometry of the universe. Under these conditions, the concept of a large-scale 'velocity' is a different one that in special relativity, because not only may a body move through its local space producing Doppler shifts, but because space is expanding, there is a second mechanism whereby the distances between particles may increase; space itself is dilating in scale. Now, the concept of a global 'velocity' is not the same as we are familiar with, and which is covered by special relativity. The 'speed' between distant points is now a complex combination of local and general relativistic effects, and special relativity no longer applies. This means that the constancy of the speed of light as a GLOBAL concept is invalidated, but locally, in a small patch of space as big as an individual galaxy, it still works well!

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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.