The age of the universe thread

Originally posted by sonhouse
Can there theoretically be some kind of field without energy? Magnetic fields have energy in the field itself, same with electric fields, electromagnetic fields contains energy, gravitational fields contains energy as does gravity waves.

How can there be any kind of 'field' that contains no energy?

The key to this is to recall what we mean by energy. If you apply a force to a body and it moves some distance then you have done some work on it and the work done is the product of the force and the distance travelled. So we introduce this abstract quantity called energy the amount of which transferred during some interaction between two objects is the work done by one object on the other. This means that something with no energy can do no work.

In the case of a field, if there were no energy that could be associated with it then it could do no work. So to a first order approximation a field without energy cannot be observed or ever influence anything else. In other words you can assume it is present or absent and never tell the difference.

The caveat to that is the Higgs vacuum. The vacuum state has a non-zero value for the field, but by definition no energy. Because of the way the other fields couple to the ground state they gain mass. So we have an energy free field (it's in its ground state) exerting physical influence on the rest of the universe. But the Higgs field can be put into an excited state and it will be out of its vacuum state and there will be energy associated with that.

So a field that could never have energy basically doesn't exist. A field in its vacuum state has no energy, because it is in its lowest possible state and cannot do any work, but can influence the behaviour of other fields if its vacuum is non-trivial and can be exited out of its ground state when it will have some energy.