# Q & A: Galilean relativity

Q:
If a train runs at 100km/h and if in this train somebody drops a rubber ball and catch it, let's say it drops down 1m and up in one second, it means that the ball has travelled 2 meters in one second for the person in the train.If I am at the station looking at the train when it passes me by and let's say it is made of glass so I can see what is happening, I can see the ball dropping down and up but for me as the train is moving the ball will have travelled 2 meters plus the distance travelled by the train in one second so more than 2 meters.I don't think that space time dilatation plays at this sort of speed so how is it explained?Thanks, Mark
- Lucas (age 27)
London
A:

You're right that our common-sense rules fro translating the coordinates used by the guy on the train to the coordinates used by the guy on the ground already say that distance traveled comes out different in these two descriptions. We say that the distance between two events that aren't simultaneous isn't invariant. My favorite example is that on the train City of New Orleans the distance between dinner and breakfast is zero, since both happen in the dining car. According to the ground, dinner is in (say) Kankakee and breakfast in Jackson, a distance of several hundred miles.

The surprising aspect of Special Relativity is that neither simultaneity nor distance between simultaneous events is invariant under this sort of change of viewpoint. Instead it turns out that the speed of light is invariant, which isn't something you'd expect.

Mike W.

Note to people who don't live in Illinois:  The City of New Orleans is a train that runs between Chicago and New Orleans.  Kankakee, Champaign-Urbana, and Jackson are stops along the way.   LeeH

(published on 09/06/2015)