Conservation and forces/energy

Question

Are there really non-conservative forces in actuality ?

Feynman states in his book that in fact, all forces are conservative ( originating from conservative vector-fields ), provide we look close enough ( microscopic level ). The reasoning is that we can't allow non-conservative forces in order for Conservation of Energy to follow.

But at the same time, physicists who seem to really know the subject in an advanced-level, assert that most forces refuse to be conservative.

For instance, see acepted answer of Locally every force admits a potential?.

So, are all forces conservative forces and conservation of energy is not violated, or are there non-conservative forces and conservation of energ is violated , or finally, Law of Conservation of energy can cohexist with non-conservative forces ?

Answer 1

There are macroscopic forces that admit no description in terms of a potential, for example, any friction force proportional to the velocity of a moving object as path-dependent integral, and is hence non-conservative.

But we know the macroscopic description is not the fundamental description. In terms of the interaction of the constituents of matter, all fundamental forces known - gravity, electromagnetism, the strong and the weak force - are conservative forces in the sense that they are descended from a (gauge) potential. It is highly non-trivial (and indeed, not done for the general case as far as I know) to derive the appearance of superficially non-conservative forces from this fundamental Lagrangian description.

Nevertheless, in the spirit of reductionism, Feynman and most other physicists believe the description in terms of the fundamental forces is more or less complete - all other forces emerge in some sense from them, and so, since the underlying microscopic description conserves energy, so must the emergent macroscopic description.

Answer 2

All the known forces conserve energy, but they don't necessarily conserve energy in macroscopic modes.

For instance friction takes some of the energy of macroscopic motion and coverts it into an increase in temperature (i.e. energy in microscopic modes). Total energy is conserved but energy that is useful at the human scale is not.

Feynman is talking about all energy and introductory textbooks (and those that concern themselves with thermodynamics) use a more restrictive definition.

Just make sure you know which definition you care about.