Besides boost symmetry providing an explanation for why objects can have different states of motion while being the same structurally, I think it’s also interesting to ask why objects can be accelerated without disrupting their structure (at least for small accelerations). As you already point out, one very important part of the explanation is that the spatial arrangement of atoms in an object forms a local energy minimum. So the restoring force in response to any perturbation tries to restore the original shape of the object.
Then we can ask why you can pick up a coffee cup by the handle and alter its momentum without disrupting the cup? The response of the cup to being picked up by the handle and moved can be converted into the sum of two terms:
Rigid motion matching the motion of your hand.
Sound waves propagating through the cup. This term corrects for the fact that the motion of the cup arises from purely local interactions between its atoms.
Most of the energy you exert goes into term 1, and a good question is why this happens.
The speed of sound in the cup is fast, much faster than your movement of the handle. Equivalently, of the degrees of freedom corresponding to the relative motion of the cup’s atoms, even the slowest vibrate quickly (on the order of the time needed for sound to cross the cup and come back). So relatively less energy goes into vibrations. Here is a 1d system with harmonic potential, where the center of the potential is being moved around according to the function . When the oscillation frequency is high, less energy ends up in vibrations after the system has been accelerated. (Because the perturbation of the system is spread out in time and so there is a lot of phase cancellation.) I think the math here is related to the adiabatic theorem.
Besides boost symmetry providing an explanation for why objects can have different states of motion while being the same structurally, I think it’s also interesting to ask why objects can be accelerated without disrupting their structure (at least for small accelerations). As you already point out, one very important part of the explanation is that the spatial arrangement of atoms in an object forms a local energy minimum. So the restoring force in response to any perturbation tries to restore the original shape of the object.
Then we can ask why you can pick up a coffee cup by the handle and alter its momentum without disrupting the cup? The response of the cup to being picked up by the handle and moved can be converted into the sum of two terms:
Rigid motion matching the motion of your hand.
Sound waves propagating through the cup. This term corrects for the fact that the motion of the cup arises from purely local interactions between its atoms.
Most of the energy you exert goes into term 1, and a good question is why this happens.
The speed of sound in the cup is fast, much faster than your movement of the handle. Equivalently, of the degrees of freedom corresponding to the relative motion of the cup’s atoms, even the slowest vibrate quickly (on the order of the time needed for sound to cross the cup and come back). So relatively less energy goes into vibrations. Here is a 1d system with harmonic potential, where the center of the potential is being moved around according to the function