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I once traveled from Vladivostok to Moscow by train

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?

And the linked post reminded me of a question that arose while riding the train. At the time, I tried to communicate my question to some nice Tajik people (is that the right term for people from Tajikistan?) by literally drawing shapes in the dust on the Siberian prairie, since we didn't have a common language.

Traveling from Vladivostok to Moscow takes you in the same direction as the sun from our perspective. Does that mean that there is a theoretical speed at which the train could've moved and at which the perceived time of day doesn't pass*? If so, what constants and variables do I need to learn about in order to make the calculations? Earth's rotation? The trains speed?

*while time of course passes on it's own, in the sense that I am still approach my impending death in some decades.

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