I don't know about Amtrak, but other country's railway companies offer this:

http://reiseauskunft.bahn.de/bin/bhftafel.exe/dn?
enter a station name (for example "Frankfurt(Main)Hbf")Select Abfahrt (departures) or Ankunft (arrivals) and click on "Anzeigen"."pünktlich" = "on time", otherwise it shows how late the train is.

Alternatively: http://map.search.ch/
Double-click on the map to zoom onto the town or city of your choice. Once you have zoomed enough, you will see symbols for railway stations and bus stops. Hover your mouse over the symbol and you will see current departures for that bus stop or station.

Sounds like a good tool for terrorists. Bad Idea.

Are you going to stop issuing timetables as well, because they are also useful to terrorists?
And ban shops displaying opening hours (that tells the terrorists when people will be in them)?