Leslie asked me a physics question a couple days ago that I didn't know how to answer, and I am still thinking about it, so I'm posting it here for others to ponder.
Why do we say that electric/magnetic/gravitational energy is in the field, when the energy is actually in the interaction between two objects, and the field is the thing we define to eliminate the second object and therefore does not include the interaction? In other words, the electric energy term has a q^2 in it, to include the electric interaction between two charges, but the electric field term only has a q in it because it only includes one charge. You can have an electric field even if you have only one charge that is not interacting with anything. But do you have electric energy is you have only one charge that is not interacting with anything? I don't think so. If this were true, the energy would be in the individual charges (or spread around them, but still belonging to them), rather than in the interaction between charges.
Why do we say that electric/magnetic/gravitational energy is in the field, when the energy is actually in the interaction between two objects, and the field is the thing we define to eliminate the second object and therefore does not include the interaction? In other words, the electric energy term has a q^2 in it, to include the electric interaction between two charges, but the electric field term only has a q in it because it only includes one charge. You can have an electric field even if you have only one charge that is not interacting with anything. But do you have electric energy is you have only one charge that is not interacting with anything? I don't think so. If this were true, the energy would be in the individual charges (or spread around them, but still belonging to them), rather than in the interaction between charges.
Here's how I think about it. Q is the property of the charge that allows it the "couple" the electric field... so q is a measure of how much energy it can "tap" out of the field. The energy is in the field, and q tells you how *good* it is at putting energy in or taking energy out of the field as it moves.
ReplyDeleteSame for m, when you raise the mass, you *strain* the gravitational field and energy gets distributed across the field. So, let's imagine you raise two masses m and M, to same height. Raising those masses, reconfigures the gravitational field, causing energy to be stored in the strain that this has produced. If you let go of little m, it will fall and speed up, but little m can't tap into all the energy in the field. For example, little m can't get the extra energy that M has put into the field, because m limits the amount of energy it can pull out of the field.
So charge and mass you can think of as "energy tappability" constants.
Two thoughts:
ReplyDelete1) Sam says "You can have an electric field even if you have only one charge that is not interacting with anything. But do you have electric energy if you have only one charge that is not interacting with anything? I don't think so." It sounds to me like you are proposing that the existence of an electric field implies the existence of electric energy in the field - that you can't have a field without energy in the field. I'm not making any claims as to the correctness or incorrectness of Sam's statement I'm just making explicit something that seems to me to be implied in this statement.
2) I never took quantum field theory but my understanding is that in QFT particles are simply exitations in the field. In this case I wonder if a particle physicist would say that 'energy in the field', 'energy in the interaction' and 'energy shared between the particles' all mean the same thing.