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I’ve been thinking about a question that blends solid mechanics and relativity, and I’d love to hear your thoughts.

When a solid object is accelerated from rest to a velocity , internal stresses propagate through it at a finite speed, leading to transient deformations. If damping is negligible, these stresses can induce sustained internal oscillations. Since internal energy contributes to an object’s rest mass, would these persistent oscillations lead to an increase in the object's rest mass as long as they remain?

Taking this further, let’s say we accelerate the object to some velocity and then bring it back to rest. If there is no damping, the oscillations generated during acceleration should continue indefinitely, meaning that the object—despite being at rest again—would retain a permanently increased rest mass. This would imply a kind of memory effect, where an object's rest mass carries information about its past accelerations.

If this reasoning is correct, could this effect provide a way to distinguish elementary particles from composite ones? Elementary particles, being structureless, should not exhibit such changes in rest mass, whereas composite particles—such as hadrons, with their internal quark-gluon dynamics—could, in principle, store residual energy in internal excitations. Could this be experimentally tested by examining subtle mass variations in hadrons or other composite systems with different excitation histories?

I’ve looked for literature on this topic but haven’t found anything definitive. I’d love to hear if this idea has been explored before or if there are fundamental reasons why it wouldn’t work. Any insights would be greatly appreciated!

Qmechanic
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Dhragva
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2 Answers2

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You don't need to accelerate a body to a velocity to increase its rest mass. Suppose you have a bell, and hit it from opposite sides with a pair of hammers. It doesn't gain any velocity, but the ringing is added energy, so its rest mass increases. You could also heat it up without moving it, and that would also increase its rest mass. So the increase in rest mass can be considered separately from the change in velocity, and may be why you can't find anything.

It would be similar for elementary particles. Familiar examples would be individual atoms. An atom with its electrons not all in their ground state will have a higher rest mass than one where they are all in the ground state. The nucleus could also be in an excited state, and might be closest to what you are thinking about. See the Nuclear Isomer page on Wikipedia from some interesting reading.

BaddDadd
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Yes, this can happen. And you do not even need oscillation. If you accelerate an object from one end, that will introduce stress, either tension or compression. This shows up in the stress energy tensor. If the spacetime is flat this can be integrated to get the four-momentum, and hence the rest mass.

As you suggest, an excited state will have more mass than the ground state. And excited states do imply that there is some internal structure. Measurements of the excited state can be done during the time it persists. Although this time is often (usually) very brief.

Dale
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