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Picture this. You are sitting on the station on a train nestling your coffee, sandwich and newspaper.

That train moves off, briefly making one think one's train is moving backwards when it is not. Or - more often still - the other train is arriving so one thinks one's train is leaving already.

I know there is a German word for this, but is there an English word or phrase that succinctly describes this (neither special nor general) relativistic effect?

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    Nothing comes to mind. But then train travel is not particularly common in the US, outside of the subways.
    – Hot Licks
    Aug 8 '20 at 20:54
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    It’s not limited to trains though. As teens we used to pull up in either side of someone at the light. And then we’d both slowly roll backwards causing the other driver to panic as the thought they were rolling forward into the intersection.
    – Jim
    Aug 9 '20 at 3:45
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    @jim We used to do the same thing standing at the curb waiting for a bus. We would stand on opposite sides of someone and start to sway in unison.
    – Phil Sweet
    Aug 15 '20 at 0:27
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"Visually induced illusory motion" is the generic term; the particular sort associated with trains is "vection" (gizmodo).

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I think that's called vection.

Vection: vection is the sensation of movement of the body in space produced purely by visual stimulation. [Encyclopedia]

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