Does Eternalism imply looping consciousness?

Question

If the idea of Eternalism as expressed by those like J.M.E. McTaggart and Sean Carroll is true (as much of physics seems to suggest), the idea of the present moment being more real than the past or future is just a biological illusion. If that's the case, then what does it mean for our consciousness to in some sense exist eternally at every moment in our lives? I have to imagine that we're continuously retreading the same path through space-time that is producing the same experience over and over, only experiencing it linearly one moment at a time because of the limitations of our perception. I see this as different from Nietzsche's idea of Eternal Recurrence; we aren't appearing in different incarnations that have identical experiences over infinite time but continually reliving the exact same experience.

Good explanation of Eternalism and Presentism here.

Edit (11/16/21): I actually posed this question to Sean Carroll last year on his monthly AMA and his answer was of course that we don't know what the implications of eternalism are for consciousness, but it has something to do with the nature of the arrow of time and the second law of thermodynamics. The link should automatically go to the correct timestamp, but if not it's 1:43:01. What he said doesn't vindicate my point but it's definitely interesting input into the discussion.

Answer 1

There is no stasis (not even the idea of stasis) without movement, and vice versa. A circulating moving spotlight of a fixed context is thus one at least coherent depiction of an eternalistic universe. What else would categorize such a universe, as gleamed by Hinton, Mach, Planck, Einstein and William James, and succinctly codified by Lawrence LeShan, can be found in a very brief essay I recently published with the Journal of Conscious Evolution

https://digitalcommons.ciis.edu/cejournal/vol17/iss1/1/

Nietzsche's compelling, robust championing of circular eternalism (minus his aborted attempt to appeal to the wrong physics--having died 5 years before Einstein's Relativity, and unaware of Hinton's Fourth Dimensional musings)--is elaborated in my book, The Illusion of Will, Self, and Time (SUNY Press).

Answer 2

I think you are misunderstanding Eternalism, which to my eyes is essentially just another way of thinking about a deterministic universe.

If the universe is deterministic, there is nothing special about the present. The present is simply the state of the universe at time t and no more or less real than the state at time t+1 or t-1

No reincarnation or repetition is implied. Its just like having a film reel, each frame is as real as any other when its not in a projector. But the film still has a beginning and an end and you only watch it once.