# The force from the energy gradient

• A
user1139
TL;DR Summary
From this post-gradient energy in classical field theory, one identifies the term ##E\equiv\frac{1}{2}\left(\partial_x\phi\right)^2## as the gradient energy which can be interpreted as elastic potential energy.

Can one then say that $$F\equiv -\frac{\partial E}{\partial\left(\partial_x\phi\right)}=-\partial_x\phi$$
is the associated force?

In addition, if one has the factor as ##2## instead of ##\frac{1}{2}##, can one just ignore the factor of ##4## and claim that the associated force is ##-\partial_x\phi## since the factor is just a scaling?

Gold Member
No and no. The second no is obvious; the force is not scale invariant, so the scale matters. To understand the first no, ask yourself: the force on what?

topsquark