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Let's say a body with m=2kg falls from 100 meters. Obviously it's speed would be far lower than the speed of light so the change in mass (if it exists) would be very tiny. However, I know that if the speed increases, its mass would increase too. That's because its kinetic energy would become bigger. On the other hand, its potential energy would decrease in the same amount that KE has increased.

Does this suggest that either the mass is not going to change (due to the conservation of energy) or it would become slightly bigger, but never less?

menislici
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2 Answers2

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I assume you are talking about 'relativistic mass', i.e $m(v)=\gamma(v) m_0$. No one really uses this notion any more because it is not quite useful to reason about this quantity as if it is a mass, so I am going to talk about the energy $E=\gamma m_0 c^2$ instead.

By $E^2= m_0^2 c^4 + |\vec{p}|^2 c^2$ we see that the energy increases as the speed increases so it should get bigger as it falls downwards.

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If you were observing the falling body alone, then it would appear to gain mass as its kinetic energy increases. However, a corresponding amount of mass would be lost from other parts of the falling object/Earth system. So, observing the falling body alone, it appears to gain mass. Observing the system as a whole, it does not.

My notion (although someone more knowledgeable about GR may correct me) is that the mass is lost from the graviton field between the two bodies.

KDN
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