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## Summary:

- does the mass of a falling object increase, decrease, or stay the same?

I'm reading Schutz's A First Course In General Relativity and in chapter 5 he discusses an idealized experiment in which an object is dropped from a tower, then turned into a photon and sent back up to its original height.

In classical mechanics we would say that as the object falls it loses potential energy and gains equal kinetic energy so at every moment its total energy is constant. In relativity, if an object gains energy its mass increases according to [itex] \Delta m = \Delta E / c^2 [/itex]. Does this apply to both kinetic and potential energy so that — as in classical mechanics — the object's mass remains constant as it falls?

On the one hand, energy can't just disappear and as I understand relativistic mechanics, [itex]E=mc^2[/itex] applies to potential energy as well as kinetic. On the other hand, the whole point of the tower thought experiment is that the object has more mass[energy] after it has fallen to its lower position.

In classical mechanics we would say that as the object falls it loses potential energy and gains equal kinetic energy so at every moment its total energy is constant. In relativity, if an object gains energy its mass increases according to [itex] \Delta m = \Delta E / c^2 [/itex]. Does this apply to both kinetic and potential energy so that — as in classical mechanics — the object's mass remains constant as it falls?

On the one hand, energy can't just disappear and as I understand relativistic mechanics, [itex]E=mc^2[/itex] applies to potential energy as well as kinetic. On the other hand, the whole point of the tower thought experiment is that the object has more mass[energy] after it has fallen to its lower position.