# B Contributions to rest energy

#### etotheipi

My physics textbook states that increasing the GPE of an object will increase its rest mass by E/c^2 , though I don't think this should be the case. I would argue that increasing the GPE of the object-Earth system will cause the rest energy of the system to increase by this amount, whilst that of the the individual object will remain unaffected. It also states that adding heat to an object, increasing its internal energy, will increase its rest mass by E/c^2; this does in fact seem to make sense.

The popular example for this is binding energies: a system of nucleons separated at large distances have a greater total mass than when they are close together in a nucleus, so we observe a mass deficit. Would I be correct in assuming that this is because the internal potential energies of the system have become more negative (i.e. assuming the particles are attracting through the strong force?).

Evidently the term rest energy is the energy in the zero momentum frame, however as of now I have just been thinking of this energy as the sum of many contributions such as internal potential energies. I have also assumed that potential energies due to external fields (e.g. gravitational) do not affect the rest energy of an object since such a potential energy is meaningless (at least at the level I am working at) without considering the whole system. I was wondering if someone could give me a more concrete definition of what constitutes the rest energy?

Taking the example of a nucleus, for instance, I would suspect that the contributions to rest energy - apart from the rest masses of each nucleon - would be internal potential energies of the nucleons, kinetic energy of the individual nucleons (not the KE of the nucleus, which would instead make up the other part of the overall relativistic energy), rotational energy of nucleons etc.

Am I thinking along the right lines?

N.B. I should also add that the intrinsic energies associated with the masses of the e.g. particles in the nucleus will contribute to rest energy, however these alone are not sufficient to explain why rest energies can change.

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#### anorlunda

Mentor
Gold Member
Are you sure he meant rest mass? Possibly he said or meant invariant mass.

#### etotheipi

Are you sure he meant rest mass? Possibly he said or meant invariant mass.

I was under the impression that rest mass and invariant mass were the same quantity m0. I could be wrong though since I'm not well versed in this field.

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#### Nugatory

Mentor
My physics textbook states that increasing the GPE of an object will increase its rest mass by E/c^2 , though I don't think this should be the case. I would argue that increasing the GPE of the object-Earth system will cause the rest energy of the system to increase by this amount, whilst that of the the individual object will remain unaffected.
Either you are misunderstanding your textbook our your textbook is wrong. And you are right that the potential energy belongs to the object-earth system and not the object in isolation.
However, increasing the GPE does not necessarily increase the rest mass of the system; that depends on where the energy to lift the object came from. For example, if we dug some coal out of the earth, burned it to make steam, used the steam to generate electricity, used the electricity to run a hoist that lifts the object to increase the GPE.... there is no change in the rest mass of the overall system because we’ve just moved energy around within the system.
together in a nucleus, so we observe a mass deficit. Would I be correct in assuming that this is because the internal potential energies of the system have become more negative (i.e. assuming the particles are attracting through the strong force?).
This one can be tricky; much more than in the earth-object-gravity case you have to be careful to track the energy that enters and leaves the system. But yes, the mass of a nucleus is generally less than sum of the masses of the same number of free nucleons, and the difference shows up in the energy released in the formation of the nucleus.

"Contributions to rest energy"

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