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Comment by brandmeyer | Hacker News Reader

> Like all potential energies, its definition is relative and its zero point convention.

Turns out that this one does have a unique definition because the limit exists, and because the sum of kinetic energy and rest mass determines the gravitational influence of a body.

> > As the body falls down the gravity well, it gains kinetic energy and loses mass.

> So you’re a saying that hydrogen lower in a gravity well will fuse worse?

No. The processes are orthogonal to each other. Forget for the moment that its the release of kinetic energy by dropping down the gravity well that makes the subsequent fusion possible at all. Whether you fused first and then dropped down the well, or dropped down the well first and then fused, the final state is the same.

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> the sum of kinetic energy and rest mass determines the gravitational influence of a body

No, I’m pretty sure it’s just rest mass. The gravitational force doesn’t change based on your kinetic energy.

> Whether you fused first and then dropped down the well, or dropped down the well first and then fused, the final state is the same.

Except the problem is that fusion only converts some fraction of mass into energy (while in your hypothesis potential energy is directly converted to mass), so in your case it would actually matter whether the fusing happened before or after falling in because lower in the gravity well, the mass would be less and you’d get less energy from the fusion.

> No, I’m pretty sure it’s just rest mass. The gravitational force doesn’t change based on your kinetic energy.

The energy-momentum tensor (a.k.a. stress-energy tensor) is what determines spacetime curvature, and it depends on both rest mass, kinetic energy, momentum, pressure, and shear stress.

> The gravitational force doesn’t change based on your kinetic energy.

This is not correct.

Gravity is a function of everything that has energy (see the stress energy tensor). It’s a very unusual “force” in this regard. This leads to interesting situations like a perfectly mirrored box of light (if you could have such a thing) weighing more on a scale than a box without light in it. Also, a spinning cue ball or a compressed spring weigh more than a stationary ball and an uncompressed spring. Granted, these differences are so small as to be undetectable by any equipment we could ever build, but it’s still interesting to think about.

You're right, I'm being stupid. Thanks for pointing that out!

Do materials weigh less when cooled to absolute zero?

The weight of a sample of matter depends on its total mass energy, and heat contributes to that total. If matter is cooled, it will weigh less, and vice-versa; if it is heated it will weigh more.

At the kinds of temperatures that normally exist on Earth, the thermal contribution to the total mass energy of a sample of matter is trivial, but in extremely hot conditions, like the first fractions of a second after the big bang, the situation is reversed.

> Except the problem is that fusion only converts some fraction of mass into energy

No. The energy release isn't actually driven by the mass of the reactants. Its driven by the strong and weak nuclear forces, which are in turn driven by quark color, spin, charge, and so on.

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