The notion of "weight" in relativity I have recently been involved in a rather animated discussion on another forum on the subject of "weight". To make a long story short, the scenario involved a train moving straight and unaccelerated at relativistic speeds through a uniform gravitational field, as in on the surface of the earth. There is a lead ball of a given mass m on the train. In the cabin frame, the lead ball has a well defined and constant "weight", being the gravitational force acting on it. The question was - what would an observer at the embankment determine that weight to be ? In other words, how does the gravitational force acting on the lead ball transform if going from one inertial frame to another in this scenario ? The discussion involved a well-known crank who asserted that in the embankment frame the lead ball has an increased relativistic mass, and will thus crash through the cabin floor, destroying the train. Obviously this cannot be how things play out, but at the same time I couldn't come up with the appropriate maths to show otherwise. How can this be approached, mathematically ?