- #1
arpharazon
- 24
- 0
Hi everybody,
i have a question concerning potential energy (in all its forms, which basically means all forms of energy except the kinetic one).
The kinetic energy of a system is always well defined: in the rest frame it is m² (convention c=1), in a frame moving at a relative speed v compared to the rest frame it is: p²+m². So it seems as if kinetic energy is a well defined quantity within each reference frame.
What puzzles me is this asymmetry with interaction energies: why doesn't an interacting particle have a definite potential energy within a definite reference frame, that would change when changing the reference frame?
I know quite well graduate level physics, so I am not looking for a reason like "it's only differences in potential energies that matter in the equations etc"; i know that. I'm trying to find whether there is a "deep" explanation.
I thought about this one but I'm pretty sure it is false:
take for example the gravitational potential energy. You can define a scalar potential field V, and potential energy would be mV in this case.
now think about electromagntism, you have a vector potential field A, i don't know what would eA correspond to in analogy with the gravitational field, maybe some form of potential energy too?
But I remember seing it in the Lagrangian of classical electrodynamics so that reconforts me.
The main idea is this: since interaction derive from potential fields (scalar, vector, tensor, doesn't matter), and these potential fields are not unique (we can transfrom them thanks to the interaction gauge group without changing the physics), the quantity charge * potential field (r) being the potential energy that a charged particle would have, it is not well defined neither until we fix a gauge for our potential field...
Am I a bit right or is it complete madness?
Thx for your help! :)
i have a question concerning potential energy (in all its forms, which basically means all forms of energy except the kinetic one).
The kinetic energy of a system is always well defined: in the rest frame it is m² (convention c=1), in a frame moving at a relative speed v compared to the rest frame it is: p²+m². So it seems as if kinetic energy is a well defined quantity within each reference frame.
What puzzles me is this asymmetry with interaction energies: why doesn't an interacting particle have a definite potential energy within a definite reference frame, that would change when changing the reference frame?
I know quite well graduate level physics, so I am not looking for a reason like "it's only differences in potential energies that matter in the equations etc"; i know that. I'm trying to find whether there is a "deep" explanation.
I thought about this one but I'm pretty sure it is false:
take for example the gravitational potential energy. You can define a scalar potential field V, and potential energy would be mV in this case.
now think about electromagntism, you have a vector potential field A, i don't know what would eA correspond to in analogy with the gravitational field, maybe some form of potential energy too?
But I remember seing it in the Lagrangian of classical electrodynamics so that reconforts me.
The main idea is this: since interaction derive from potential fields (scalar, vector, tensor, doesn't matter), and these potential fields are not unique (we can transfrom them thanks to the interaction gauge group without changing the physics), the quantity charge * potential field (r) being the potential energy that a charged particle would have, it is not well defined neither until we fix a gauge for our potential field...
Am I a bit right or is it complete madness?
Thx for your help! :)
