"Twice, I have read books on relativity by PhDs who said that we travel through time at the speed of light, but I can’t find those books, and I haven’t seen it written anywhere else. Can you let me know if this is right or if this is utter nonsense."

I wonder, was this question asked by the Ed Catmull (https://en.wikipedia.org/wiki/Edwin_Catmull)?

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Edit: to make this comment less useless, I'd like to point any laypeople like myself who are interested in the nature of the universe to the PBS Space Time show/YouTube channel: https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g

I'm pretty sure they have videos related to this question.