If you walk forward inside a Shinkansen car while the train is moving at top speed, does your personal momentum actually compress the distance between Tokyo and Nagoya, or are you just changing the rate at which the track grid passes beneath your shoes?

I suppose this is probably a special relativity question, but if I can set that aside and be a rube for a moment, I think it is a fun pure geometry question. Of course within the earth’s or your reference frame they are a fixed geometric distance, but within the solar reference frame they aren’t since the earth is moving. So the two endpoints both trace huge arcs over that time period, the delta between being negligible but still real. So I guess depending on which direction your headed you either increase or decrease the total distance “traveled” between the two, or any two points per unit time.

Can you finish the sentence in your title? I think I know the answer but want to make sure I’m not guessing wrong!

Have a look here, Einstein has you covered: https://www.researchgate.net/figure/Einsteins-famous-train-example-a-When-light-is-emitted-from-two-distinct-points_fig3_270830434

If talking about relativity, the distance to destination is further compressed only for your perspective, not the train’s, and not the earth’s. The amount compressed is imperceptible.

“Compress”? What?