In six Level 1 videos we visualize General Relativity with a substratum (“fabric”) that uses the same *math* as GR, the math of curved surfaces.

Here in part 3 of 6: Locally, we always measure the speed of light to be 1. Over distance, we measure it to be less than one. We also see how a gradient of light speed causes light to bend toward slower light. A breather (soliton) accelerates toward slower light.

I think this is misleading to say the speed of light is less than 1 when “measured over distance”. It is only because an erroneous “distance” is being assumed in the latter case by ignoring the actual local metric and assuming a Euclidean metric “over distance”.

You are correct that local measurements (short device in video) always yield c=1, while a non-local measurement (long device) can yield other values. I don’t know why it would be misleading to explore the two cases. One could argue that textbooks that don’t mention “c=1 refers to local measurements” are misleading. Some textbooks do point out the difference, for example Taylor and Wheeler’s “Exploring Black Holes” — they dedicate an entire chapter to what they call “slow light.” It’s just an alternative approach to analyzing problems.

https://media.giphy.com/media/3rUbe17ArZBziEJ8kk/giphy.gif